SSC CGL Previous Year Questions (2023-19): Mixture and Alligation | SSC CGL Mathematics Previous Year Paper (Topic-wise) PDF Download

 Page 1


 Pinnacle  Day: 54th  Mixture and Alligation 
 Mixture and Alligation 
 Mixture  :  when  two  or  more  than  two 
 substances  mixed  together  in  any  ratio  to 
 produce a product is called mixture . 
 Mean  price  :  the  average  of  all  the  given 
 prices  of  the  known  items  is  called  Mean 
 Price . 
 1.  Alligation  rule  :  It  is  used  to  ?nd  the 
 ratio  in  which  two  or  more  substances  at 
 their  respective  prices  should  be  mixed 
 to produce a mixture at a given price. 
 where 
 C = Cost price of cheaper 
 D = Cost price of dearer 
 M = Mean price 
 (D - M) = Cheaper quantity 
 (M - C) = Dearer quantity 
 2. Quantity of pure liquid  =  ?? (
 ??    -    ?? 
 ?? 
)
 ?? 
 where,  =  Quantity  of  original  liquid,  =  ??  ?? 
 Quantity  to  be  carried  out  and  replaced,  ?? 
 =  Number  of  times  the  operation  is 
 conducted 
 Important Cases :- 
 Case 1  : 
 Ratio  of  milk  and  water  in  container  A,  B 
 and  C  are  1  :  2,  4  :  1  and  4  :  5 
 respectively.  Find  the  ratio  in  which 
 containers  A  and  B  are  mixed  to  get  4  :  5 
 in container C ? 
 Soln :  Fraction of milk in container A = 
 1 
 3 
 Fraction of milk in container B = 
 4 
 5 
 Fraction of milk in container C = 
 4 
 9 
 So, the required ratio = 16 : 5 
 Case 2  : 
 Ratio  of  milk  and  water  in  container  A 
 and  B  are  3  :  1  and  4  :  1  respectively. 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  Find  the  ratio  of 
 quantity of milk and water in container C. 
 Soln : 
 Fraction of milk in container A = 
 3 
 4 
 Fraction of milk in container B = 
 4 
 5 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  So,  let  the  quantity  in 
 container  A  and  B  be  2  litre  and  1  litre 
 respectively. 
 So, the required ratio = 
 [  2  ]  +  [  1] : [  2]  +  [  1] 
 3 
 4 
×
 4 
 5 
×
 1 
 4 
×
 1 
 5 
×
 =  +  :  +  =  :  = 23 : 7 
 3 
 2 
 4 
 5 
 1 
 2 
 1 
 5 
 23 
 10 
 7 
 10 
 Case  3  :  Two  varieties  costing  ?4/kg  and 
 ?5/kg  respectively  are  mixed  in  3  :  2.  Find 
 the  cost  price  per  kg  of  the  resultant 
 mixture? 
 Soln: 
 A 
 wt 
 =  = 
 ??  1  ??  1    +    ??  2  ??  2 
 ??  1    +    ??  2 
 4     ×     3    +    5     ×     2 
 3    +    2 
 =  =  = 4.4 kg 
 12    +    10 
 5 
 22 
 5 
 Variety Questions 
 Q.1.  80  litres  of  a  mixture  of  spirit  and 
 water  in  the  ratio  7  :  9  is  present  in  a 
 container  A.  20  litres  of  the  mixture  is 
 transferred  to  another  container  B.  Then 
 the  container  A  is  ?lled  with  20  litres  of 
 water.  Then  32  litres  of  the  mixture  is 
 again  transferred  to  container  B.  The 
 ratio  of  water  to  spirit  of  the  mixture  in 
 container B is equal to: 
 SSC CGL Tier II  (26/10/2023) 
 (a) 41 : 87  (b) 87 : 41 
 (c) 131 : 77  (d) 77 : 131 
 Q.2.  At  a  certain  time  in  a  park,  the 
 number  of  heads  and  the  number  of  legs 
 of  monkeys  and  human  visitors  were 
 counted,  and  it  was  found  that  there  were 
 54  heads  and  148  legs.  Find  the  number 
 of monkeys in the park. 
 SSC CGL Tier II  (26/10/2023) 
 (a) 20  (b) 16  (c) 18  (d) 14 
 Q.3.  A  milk  vendor  has  2  vessels  of  milk 
 and  water.  The  ?rst  contains  80%  milk 
 and  the  rest  is  water.  The  second 
 contains  50%  milk.  How  much  mixture  (in 
 L)  should  he  mix  from  each  of  the 
 vessels  so  as  to  get  9  litres  of  mixture 
 such  that  the  ratio  of  water  to  milk  is  1  :  2 
 ?  (Write  your  answer  in  the  order  of 
 vessel 1 and vessel 2) 
 SSC MTS 13/09/2023 (1st Shift) 
 (a) 6, 3  (b) 4, 5  (c) 3, 6  (d) 5, 4 
 Q.4.  A  blended  tea  in  a  barrel  contains 
 Assam,  Darjeeling  and  Nilgiri  Hills  in  the 
 ratio  2  :  3  :  1.  Another  barrel  contains 
 Darjeeling,  Nilgiri  Hills  and  Kangra  Valley 
 in  the  ratio  5  :  4  :  3.  If  equal  weights  of 
 both  blended  tea  mix  together  to  make  a 
 new brand, then the weight of Kangra 
 Valley per kilogram in the new brand is: 
 SSC CHSL 10/08/2023 (3rd Shift) 
 (a) 500 gm  (b) 100 gm 
 (c) 250 gm  (d) 125 gm 
 Q.5.  From  a  cask  of  milk  containing  64 
 liters,  8  liters  are  drawn  out  and  the  cask 
 is  ?lled  up  with  water.  If  the  same 
 process  is  repeated  a  second,  then  a 
 third  time,  what  will  be  the  proportion  of 
 milk to water in the resulting mixture ? 
 SSC CHSL 09/08/2023 (2nd Shift) 
 (a) 343 : 179  (b) 333 : 169 
 (c) 443 : 179  (d) 343 : 169 
 Q.6.  A  jar  contains  35%  syrup  in  the 
 mixture  of  syrup  and  water.  A  part  of  this 
 mixture  is  replaced  by  another  mixture 
 containing  20%  syrup.  Now,  in  the  new 
 mixture,  the  percentage  of  syrup  is  found 
 to  be  24%.  What  is  the  ratio  in  which 
 these  mixtures  were  mixed  to  obtain  the 
 new mixture ? 
 SSC CHSL 07/08/2023 (2nd Shift) 
 (a) 3 : 14  (b) 4 : 11  (c) 5 : 13  (d) 7 : 10 
 Q.7.  In  a  solution  of  water  and  milk,  the 
 quantity  of  milk  is  double  the  quantity  of 
 water.  To  pass  the  quality  standards,  the 
 solution  must  contain  90%  milk  in  it.  If 
 the  volume  of  the  solution  is  v,  then  how 
 much  pure  milk  in  litres  is  to  be  added  to 
 the solution to pass the quality standard. 
 SSC CHSL 02/08/2023 (2nd Shift) 
 (a)  v  (b)  v  (c)  v  (d)  v 
 4 
 3 
 3 
 4 
 7 
 4 
 7 
 3 
 Q.8.  A  vessel  is  ?lled  with  liquid,  5  parts 
 of  which  are  water  and  11  parts  syrup. 
 What  part  of  the  mixture  must  be  drawn 
 off  and  replaced  with  water  so  that  the 
 mixture  may  be  syrup  and  water  in  the 
 ratio 3 : 2 ? 
 SSC CGL 26/07/2023 (1st shift) 
 (a)  (b)  (c)  (d) 
 14 
 45 
 27 
 35 
 36 
 65 
 7 
 55 
 Q.9.  Alloy  X  contains  70%  copper  and 
 30%  zinc.  Alloy  Y  contains  40%  copper, 
 25%  zinc  and  35%  aluminum.  Alloy  X  and 
 Y  are  mixed  in  the  ratio  of  1  :  3.  What  is 
 the  ratio  of  copper  and  zinc  in  the  newly 
 formed alloy ? 
 SSC MTS 17/05/2023 (Afternoon) 
 (a) 19 : 33  (b) 11 : 32 
 (c) 38 : 21  (d) 19 : 21 
 Q.10.  A  jar  contains  a  mixture  of  milk 
 and  water,  having  50%  water.  A  part  of 
 this  mixture  is  replaced  by  another 
 mixture  having  29%  water.  The 
 percentage  of  water  in  the  jar  after 
 replacement  is  36%.  What  fraction  of  the 
 original mixture was replaced ? 
 SSC MTS 10/05/2023 (Afternoon) 
 www.ssccglpinnacle.com                                                 Download Pinnacle Exam Preparation App 351
Page 2


 Pinnacle  Day: 54th  Mixture and Alligation 
 Mixture and Alligation 
 Mixture  :  when  two  or  more  than  two 
 substances  mixed  together  in  any  ratio  to 
 produce a product is called mixture . 
 Mean  price  :  the  average  of  all  the  given 
 prices  of  the  known  items  is  called  Mean 
 Price . 
 1.  Alligation  rule  :  It  is  used  to  ?nd  the 
 ratio  in  which  two  or  more  substances  at 
 their  respective  prices  should  be  mixed 
 to produce a mixture at a given price. 
 where 
 C = Cost price of cheaper 
 D = Cost price of dearer 
 M = Mean price 
 (D - M) = Cheaper quantity 
 (M - C) = Dearer quantity 
 2. Quantity of pure liquid  =  ?? (
 ??    -    ?? 
 ?? 
)
 ?? 
 where,  =  Quantity  of  original  liquid,  =  ??  ?? 
 Quantity  to  be  carried  out  and  replaced,  ?? 
 =  Number  of  times  the  operation  is 
 conducted 
 Important Cases :- 
 Case 1  : 
 Ratio  of  milk  and  water  in  container  A,  B 
 and  C  are  1  :  2,  4  :  1  and  4  :  5 
 respectively.  Find  the  ratio  in  which 
 containers  A  and  B  are  mixed  to  get  4  :  5 
 in container C ? 
 Soln :  Fraction of milk in container A = 
 1 
 3 
 Fraction of milk in container B = 
 4 
 5 
 Fraction of milk in container C = 
 4 
 9 
 So, the required ratio = 16 : 5 
 Case 2  : 
 Ratio  of  milk  and  water  in  container  A 
 and  B  are  3  :  1  and  4  :  1  respectively. 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  Find  the  ratio  of 
 quantity of milk and water in container C. 
 Soln : 
 Fraction of milk in container A = 
 3 
 4 
 Fraction of milk in container B = 
 4 
 5 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  So,  let  the  quantity  in 
 container  A  and  B  be  2  litre  and  1  litre 
 respectively. 
 So, the required ratio = 
 [  2  ]  +  [  1] : [  2]  +  [  1] 
 3 
 4 
×
 4 
 5 
×
 1 
 4 
×
 1 
 5 
×
 =  +  :  +  =  :  = 23 : 7 
 3 
 2 
 4 
 5 
 1 
 2 
 1 
 5 
 23 
 10 
 7 
 10 
 Case  3  :  Two  varieties  costing  ?4/kg  and 
 ?5/kg  respectively  are  mixed  in  3  :  2.  Find 
 the  cost  price  per  kg  of  the  resultant 
 mixture? 
 Soln: 
 A 
 wt 
 =  = 
 ??  1  ??  1    +    ??  2  ??  2 
 ??  1    +    ??  2 
 4     ×     3    +    5     ×     2 
 3    +    2 
 =  =  = 4.4 kg 
 12    +    10 
 5 
 22 
 5 
 Variety Questions 
 Q.1.  80  litres  of  a  mixture  of  spirit  and 
 water  in  the  ratio  7  :  9  is  present  in  a 
 container  A.  20  litres  of  the  mixture  is 
 transferred  to  another  container  B.  Then 
 the  container  A  is  ?lled  with  20  litres  of 
 water.  Then  32  litres  of  the  mixture  is 
 again  transferred  to  container  B.  The 
 ratio  of  water  to  spirit  of  the  mixture  in 
 container B is equal to: 
 SSC CGL Tier II  (26/10/2023) 
 (a) 41 : 87  (b) 87 : 41 
 (c) 131 : 77  (d) 77 : 131 
 Q.2.  At  a  certain  time  in  a  park,  the 
 number  of  heads  and  the  number  of  legs 
 of  monkeys  and  human  visitors  were 
 counted,  and  it  was  found  that  there  were 
 54  heads  and  148  legs.  Find  the  number 
 of monkeys in the park. 
 SSC CGL Tier II  (26/10/2023) 
 (a) 20  (b) 16  (c) 18  (d) 14 
 Q.3.  A  milk  vendor  has  2  vessels  of  milk 
 and  water.  The  ?rst  contains  80%  milk 
 and  the  rest  is  water.  The  second 
 contains  50%  milk.  How  much  mixture  (in 
 L)  should  he  mix  from  each  of  the 
 vessels  so  as  to  get  9  litres  of  mixture 
 such  that  the  ratio  of  water  to  milk  is  1  :  2 
 ?  (Write  your  answer  in  the  order  of 
 vessel 1 and vessel 2) 
 SSC MTS 13/09/2023 (1st Shift) 
 (a) 6, 3  (b) 4, 5  (c) 3, 6  (d) 5, 4 
 Q.4.  A  blended  tea  in  a  barrel  contains 
 Assam,  Darjeeling  and  Nilgiri  Hills  in  the 
 ratio  2  :  3  :  1.  Another  barrel  contains 
 Darjeeling,  Nilgiri  Hills  and  Kangra  Valley 
 in  the  ratio  5  :  4  :  3.  If  equal  weights  of 
 both  blended  tea  mix  together  to  make  a 
 new brand, then the weight of Kangra 
 Valley per kilogram in the new brand is: 
 SSC CHSL 10/08/2023 (3rd Shift) 
 (a) 500 gm  (b) 100 gm 
 (c) 250 gm  (d) 125 gm 
 Q.5.  From  a  cask  of  milk  containing  64 
 liters,  8  liters  are  drawn  out  and  the  cask 
 is  ?lled  up  with  water.  If  the  same 
 process  is  repeated  a  second,  then  a 
 third  time,  what  will  be  the  proportion  of 
 milk to water in the resulting mixture ? 
 SSC CHSL 09/08/2023 (2nd Shift) 
 (a) 343 : 179  (b) 333 : 169 
 (c) 443 : 179  (d) 343 : 169 
 Q.6.  A  jar  contains  35%  syrup  in  the 
 mixture  of  syrup  and  water.  A  part  of  this 
 mixture  is  replaced  by  another  mixture 
 containing  20%  syrup.  Now,  in  the  new 
 mixture,  the  percentage  of  syrup  is  found 
 to  be  24%.  What  is  the  ratio  in  which 
 these  mixtures  were  mixed  to  obtain  the 
 new mixture ? 
 SSC CHSL 07/08/2023 (2nd Shift) 
 (a) 3 : 14  (b) 4 : 11  (c) 5 : 13  (d) 7 : 10 
 Q.7.  In  a  solution  of  water  and  milk,  the 
 quantity  of  milk  is  double  the  quantity  of 
 water.  To  pass  the  quality  standards,  the 
 solution  must  contain  90%  milk  in  it.  If 
 the  volume  of  the  solution  is  v,  then  how 
 much  pure  milk  in  litres  is  to  be  added  to 
 the solution to pass the quality standard. 
 SSC CHSL 02/08/2023 (2nd Shift) 
 (a)  v  (b)  v  (c)  v  (d)  v 
 4 
 3 
 3 
 4 
 7 
 4 
 7 
 3 
 Q.8.  A  vessel  is  ?lled  with  liquid,  5  parts 
 of  which  are  water  and  11  parts  syrup. 
 What  part  of  the  mixture  must  be  drawn 
 off  and  replaced  with  water  so  that  the 
 mixture  may  be  syrup  and  water  in  the 
 ratio 3 : 2 ? 
 SSC CGL 26/07/2023 (1st shift) 
 (a)  (b)  (c)  (d) 
 14 
 45 
 27 
 35 
 36 
 65 
 7 
 55 
 Q.9.  Alloy  X  contains  70%  copper  and 
 30%  zinc.  Alloy  Y  contains  40%  copper, 
 25%  zinc  and  35%  aluminum.  Alloy  X  and 
 Y  are  mixed  in  the  ratio  of  1  :  3.  What  is 
 the  ratio  of  copper  and  zinc  in  the  newly 
 formed alloy ? 
 SSC MTS 17/05/2023 (Afternoon) 
 (a) 19 : 33  (b) 11 : 32 
 (c) 38 : 21  (d) 19 : 21 
 Q.10.  A  jar  contains  a  mixture  of  milk 
 and  water,  having  50%  water.  A  part  of 
 this  mixture  is  replaced  by  another 
 mixture  having  29%  water.  The 
 percentage  of  water  in  the  jar  after 
 replacement  is  36%.  What  fraction  of  the 
 original mixture was replaced ? 
 SSC MTS 10/05/2023 (Afternoon) 
 www.ssccglpinnacle.com                                                 Download Pinnacle Exam Preparation App 351
 Pinnacle  Day: 54th  Mixture and Alligation 
 (a)  (b)  (c)  (d) 
 3 
 2 
 4 
 5 
 1 
 3 
 2 
 3 
 Q.11.  A  100  ml  solution  of  having  ?? 
 2 
 ???? 
 4 
 concentration  of  20%  is  mixed  with  a 
 50%  concentrated  x  ml  mixture  such  that 
 the  net  mixture  is  30%  concentrated. 
 Determine x. 
 SSC CGL  08/12/2022 (1st Shift) 
 (a) 70 ml  (b) 80 ml  (c) 60 ml  (d) 50 ml 
 Q.12.  The  cost  of  two  varieties  of  tea  is 
 ?300  and  ?375  respectively.  If  both  the 
 varieties  of  tea  are  mixed  together  in  the 
 ratio  3  :  2,  then  what  should  be  the  price 
 of the mixed variety of tea per kg? 
 SSC CPO 09/11/2022 (Morning) 
 (a) ?340 (b) ?330 (c) ?350 (d) ?360 
 Q.13.  Two  vessels  of  equal  capacity,  and 
 both  completely  ?lled,  contain  mixtures 
 of  milk  and  water  in  the  ratio  5  :  1  and  6  : 
 5,  respectively.  Both  the  mixtures  are 
 now  mixed  thoroughly.  What  is  the  ratio 
 of  milk  to  water  in  the  new  mixture  so 
 obtained? 
 SSC MTS 13/07/2022 (Evening) 
 (a) 105 : 67  (b) 57 : 41 
 (c) 91 : 41  (d) 28 : 43 
 Q.14.  Babulal  runs  a  juice  corner  outside 
 a  park  and  sells  giloy  juice  (giloy  +  water) 
 in  the  morning.  Initially  he  had  19  litres  of 
 juice,  which  had  giloy  and  water  in  the 
 ratio  2  :  9.  He  sold  2  litres  of  juice. 
 1 
 2 
 Later,  in  order  to  dilute  it,  he  added  some 
 water  and  the  ratio  of  giloy  and  water 
 became  1  :  5.  How  much  water  was 
 added ? 
 SSC MTS 27/10/2021 (Morning) 
 (a) 1  litres  (b)  litre 
 1 
 2 
 1 
 2 
 (c)  2 litres  (d) 1 litre 
 Q.15.  Alloy  A  contains  metal  x  and  y  only 
 in  the  ratio  5  :  2  and  alloy  B  contains 
 these  metals  in  the  ratio  3  :  4.  Alloy  C  is 
 prepared by mixing A and B in the ratio 
 4 : 5. The percentage of x in alloy C is: 
 SSC CGL Tier II (16/11/2020) 
 (a) 44  (b) 56  (c) 45  (d) 55 
 4 
 9 
 5 
 9 
 Q.16.  Two  bottles  of  same  capacity  are 
 35%  and  33  %  full  of  orange  juice, 
 1 
 3 
 respectively.  They  are  ?lled  up 
 completely  with  apple  juice  and  then  the 
 contents  of  both  bottles  are  emptied  into 
 another  vessel.  The  percentage  of  apple 
 juice in the mixture is: 
 SSC CGL 03/03/2020 (Afternoon) 
 (a) 34  (b) 64  (c) 60  (d) 65 
 1 
 6 
 1 
 3 
 2 
 3 
 5 
 6 
 Q.17.  A  vessel  contains  a  32  litre 
 solution  of  acid  and  water  in  which  the 
 ratio  of  acid  and  water  is  5  :  3.  If  12  litres 
 of  the  solution  are  taken  out  and  7 
 1 
 2 
 litres  of  water  are  added  to  it,  then  what 
 is  the  ratio  of  acid  and  water  in  the 
 resulting solution ? 
 SSC CGL Tier II (13/09/2019) 
 (a) 4 : 7  (b) 5 : 6  (c) 4 : 9  (d) 8 : 11 
 Q.18.  The  ratios  of  copper  to  Zinc  in  alloys 
 A  and  B  are  3  :  4  and  5  :  9  respectively.  A 
 and  B  are  taken  in  the  ratio  2:3  and  melted 
 to  form  a  new  alloy  C.  What  is  the  ratio  of 
 copper to Zinc in C ? 
 SSC CGL Tier II (11/09/2019) 
 (a) 8 : 13  (b) 3 : 5  (c) 9 : 11  (d) 27 : 43 
 Q.19.  A  mixture  contains  milk  and  water 
 in  the  ratio  (by  volume)  5  :  3  and  another 
 mixture,  of  the  same  volume  as  that  of 
 the  former,  contains  water  and  milk  in  the 
 ratio  (by  volume)  1  :  3.  In  what  ratio,  two 
 mixture  be  mixed  in  order  to  obtain  a  new 
 mixture  consisting  of  milk  and  water  in 
 the ratio (by volume) 7 : 3 ? 
 SSC MTS 13/08/2019 (Afternoon) 
 (a) 2 : 3  (b) 3 : 4  (c) 5 : 6  (d) 3 : 2 
 Q.20.  In  the  60  litre  mixture  of  milk  and 
 water,  the  quantities  of  milk  and  water 
 are  in  the  ratio  of  3  :  2.  If  we  want  to 
 make  the  ratio  of  the  quantities  of  milk 
 and  water  1  :  1,  then  how  much  extra 
 water should be put in the mixture ? 
 SSC MTS 05/08/2019 (Afternoon) 
 (a)10 litre (b) 16litre  (c)12 litre (d)14 litre 
 Q.21.  A  milkman  uses  three  containers 
 for  selling  milk,  their  capacities  being 
 40L,  30L  and  20L  respectively.  He  ?lls 
 respectively  87.5%,  80%  and  90%  of  the 
 containers  with  a  mix  of  milk  and  water 
 in  the  ratios,  3  :  2,  5  :  1  and  7  :  2 
 respectively.  What  is  the  ratio  of  total 
 quantity  of  milk  to  that  of  water  carried 
 by him ? 
 SSC CHSL 10/07/2019 (Evening) 
 (a) 7 : 2  (b) 31 : 12   (c) 35 : 9   (d) 5 : 2 
 Q.22.  Fresh  fruit  contains  68%  water  and 
 dry  fruit  contains  20%  water.  How  much 
 dry  fruit  can  be  obtained  from  100  kg  of 
 fresh fruit 
 SSC CPO 16/03/2019 (Morning) 
 (a) 80  (b) 60  (c) 40  (d) 20 
 Practice Questions 
 SSC CPO 2023 Tier - 1 
 Q.23.  If 60 liters of a milk solution has 
 40% milk in it, then how much milk 
 should  be  added  to  make  the  milk  60%  in 
 the solution? 
 SSC CPO 03/10/2023 (3rd Shift) 
 (a) 30 liters  (b) 20 liters 
 (c) 35 liters  (d) 25 liters 
 Q.24.  Two  mixtures  A  and  B  have  the 
 following compositions: 
 Mixture  A  has  copper  and  tin  in  a  ratio  of 
 1 : 2 
 Mixture  B  has  copper  and  tin  in  a  ratio  of 
 1 : 3 
 If  equal  quantities  of  mixtures  A  and  B 
 are  used  for  producing  mixture  C,  then 
 ?nd  the  ratio  of  copper  and  tin  in  mixture 
 C. 
 SSC CPO 04/10/2023 (3rd Shift) 
 (a) 2 : 5    (b) 7 : 17    (c) 7 : 12    (d) 1 : 5 
 SSC MTS 2023 Tier -1 
 Q.25.  There  is  a  25  litre  mixture  of  milk 
 and  water,  containing  milk  and  water  in 
 the  ratio  3  :  2.  Find  the  number  of  litres  of 
 water  that  should  be  added  to  the 
 mixture  so  that  the  resultant  mixture  has 
 50% water in it. 
 SSC MTS 01/09/2023 (2nd Shift) 
 (a) 10  (b) 8  (c) 5  (d) 12 
 Q.26.  From  a  container  having  pure  milk, 
 35%  is  replaced  by  water  and  the  process 
 is  repeated  thrice.  At  the  end  of  the  third 
 operation, the purity of the milk is: 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 21  %  (b) 37  % 
 23 
 80 
 21 
 80 
 (c) 23  %  (d) 27  % 
 37 
 80 
 37 
 80 
 Q.27.  In  what  ratio  must  a  grocer  mix  two 
 varieties  of  pulses  costing  ?18  per  kg 
 and  ?22  per  kg,  respectively,  so  as  to  get 
 a mixture worth ?19.50 per kg? 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 5 : 3  (b) 5 : 1  (c) 1 : 5  (d) 5 : 2 
 Q.28.  How  many  kilograms  of  sugar  at 
 ?3.80  per  kg  must  be  mixed  with  60  kg  of 
 sugar  at  ?4.60  per  kg,  so  that  by  selling 
 the  mixture  at  ?5.20  per  kg  there  may  be 
 a gain of 30%? 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 170 kg  (b) 120 kg  (c) 160 kg (d) 180 kg 
 Q.29.  A  mixture  contains  milk  and  water 
 in  the  ratio  9  :  7.  If  it  contains  4  litres 
 more  milk  than  water,  then  ?nd  the 
 quantity of milk (in litres) in the mixture. 
 SSC MTS 04/09/2023 (1st Shift) 
 (a) 18  (b) 15  (c) 21  (d) 14 
 Q.30.  A  vessel  contains  liquid  A  and 
 liquid  B  in  the  ratio  4  :  9.  If  8  litres  of 
 liquid  A  is  added  to  the  vessel,  the  new 
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Page 3


 Pinnacle  Day: 54th  Mixture and Alligation 
 Mixture and Alligation 
 Mixture  :  when  two  or  more  than  two 
 substances  mixed  together  in  any  ratio  to 
 produce a product is called mixture . 
 Mean  price  :  the  average  of  all  the  given 
 prices  of  the  known  items  is  called  Mean 
 Price . 
 1.  Alligation  rule  :  It  is  used  to  ?nd  the 
 ratio  in  which  two  or  more  substances  at 
 their  respective  prices  should  be  mixed 
 to produce a mixture at a given price. 
 where 
 C = Cost price of cheaper 
 D = Cost price of dearer 
 M = Mean price 
 (D - M) = Cheaper quantity 
 (M - C) = Dearer quantity 
 2. Quantity of pure liquid  =  ?? (
 ??    -    ?? 
 ?? 
)
 ?? 
 where,  =  Quantity  of  original  liquid,  =  ??  ?? 
 Quantity  to  be  carried  out  and  replaced,  ?? 
 =  Number  of  times  the  operation  is 
 conducted 
 Important Cases :- 
 Case 1  : 
 Ratio  of  milk  and  water  in  container  A,  B 
 and  C  are  1  :  2,  4  :  1  and  4  :  5 
 respectively.  Find  the  ratio  in  which 
 containers  A  and  B  are  mixed  to  get  4  :  5 
 in container C ? 
 Soln :  Fraction of milk in container A = 
 1 
 3 
 Fraction of milk in container B = 
 4 
 5 
 Fraction of milk in container C = 
 4 
 9 
 So, the required ratio = 16 : 5 
 Case 2  : 
 Ratio  of  milk  and  water  in  container  A 
 and  B  are  3  :  1  and  4  :  1  respectively. 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  Find  the  ratio  of 
 quantity of milk and water in container C. 
 Soln : 
 Fraction of milk in container A = 
 3 
 4 
 Fraction of milk in container B = 
 4 
 5 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  So,  let  the  quantity  in 
 container  A  and  B  be  2  litre  and  1  litre 
 respectively. 
 So, the required ratio = 
 [  2  ]  +  [  1] : [  2]  +  [  1] 
 3 
 4 
×
 4 
 5 
×
 1 
 4 
×
 1 
 5 
×
 =  +  :  +  =  :  = 23 : 7 
 3 
 2 
 4 
 5 
 1 
 2 
 1 
 5 
 23 
 10 
 7 
 10 
 Case  3  :  Two  varieties  costing  ?4/kg  and 
 ?5/kg  respectively  are  mixed  in  3  :  2.  Find 
 the  cost  price  per  kg  of  the  resultant 
 mixture? 
 Soln: 
 A 
 wt 
 =  = 
 ??  1  ??  1    +    ??  2  ??  2 
 ??  1    +    ??  2 
 4     ×     3    +    5     ×     2 
 3    +    2 
 =  =  = 4.4 kg 
 12    +    10 
 5 
 22 
 5 
 Variety Questions 
 Q.1.  80  litres  of  a  mixture  of  spirit  and 
 water  in  the  ratio  7  :  9  is  present  in  a 
 container  A.  20  litres  of  the  mixture  is 
 transferred  to  another  container  B.  Then 
 the  container  A  is  ?lled  with  20  litres  of 
 water.  Then  32  litres  of  the  mixture  is 
 again  transferred  to  container  B.  The 
 ratio  of  water  to  spirit  of  the  mixture  in 
 container B is equal to: 
 SSC CGL Tier II  (26/10/2023) 
 (a) 41 : 87  (b) 87 : 41 
 (c) 131 : 77  (d) 77 : 131 
 Q.2.  At  a  certain  time  in  a  park,  the 
 number  of  heads  and  the  number  of  legs 
 of  monkeys  and  human  visitors  were 
 counted,  and  it  was  found  that  there  were 
 54  heads  and  148  legs.  Find  the  number 
 of monkeys in the park. 
 SSC CGL Tier II  (26/10/2023) 
 (a) 20  (b) 16  (c) 18  (d) 14 
 Q.3.  A  milk  vendor  has  2  vessels  of  milk 
 and  water.  The  ?rst  contains  80%  milk 
 and  the  rest  is  water.  The  second 
 contains  50%  milk.  How  much  mixture  (in 
 L)  should  he  mix  from  each  of  the 
 vessels  so  as  to  get  9  litres  of  mixture 
 such  that  the  ratio  of  water  to  milk  is  1  :  2 
 ?  (Write  your  answer  in  the  order  of 
 vessel 1 and vessel 2) 
 SSC MTS 13/09/2023 (1st Shift) 
 (a) 6, 3  (b) 4, 5  (c) 3, 6  (d) 5, 4 
 Q.4.  A  blended  tea  in  a  barrel  contains 
 Assam,  Darjeeling  and  Nilgiri  Hills  in  the 
 ratio  2  :  3  :  1.  Another  barrel  contains 
 Darjeeling,  Nilgiri  Hills  and  Kangra  Valley 
 in  the  ratio  5  :  4  :  3.  If  equal  weights  of 
 both  blended  tea  mix  together  to  make  a 
 new brand, then the weight of Kangra 
 Valley per kilogram in the new brand is: 
 SSC CHSL 10/08/2023 (3rd Shift) 
 (a) 500 gm  (b) 100 gm 
 (c) 250 gm  (d) 125 gm 
 Q.5.  From  a  cask  of  milk  containing  64 
 liters,  8  liters  are  drawn  out  and  the  cask 
 is  ?lled  up  with  water.  If  the  same 
 process  is  repeated  a  second,  then  a 
 third  time,  what  will  be  the  proportion  of 
 milk to water in the resulting mixture ? 
 SSC CHSL 09/08/2023 (2nd Shift) 
 (a) 343 : 179  (b) 333 : 169 
 (c) 443 : 179  (d) 343 : 169 
 Q.6.  A  jar  contains  35%  syrup  in  the 
 mixture  of  syrup  and  water.  A  part  of  this 
 mixture  is  replaced  by  another  mixture 
 containing  20%  syrup.  Now,  in  the  new 
 mixture,  the  percentage  of  syrup  is  found 
 to  be  24%.  What  is  the  ratio  in  which 
 these  mixtures  were  mixed  to  obtain  the 
 new mixture ? 
 SSC CHSL 07/08/2023 (2nd Shift) 
 (a) 3 : 14  (b) 4 : 11  (c) 5 : 13  (d) 7 : 10 
 Q.7.  In  a  solution  of  water  and  milk,  the 
 quantity  of  milk  is  double  the  quantity  of 
 water.  To  pass  the  quality  standards,  the 
 solution  must  contain  90%  milk  in  it.  If 
 the  volume  of  the  solution  is  v,  then  how 
 much  pure  milk  in  litres  is  to  be  added  to 
 the solution to pass the quality standard. 
 SSC CHSL 02/08/2023 (2nd Shift) 
 (a)  v  (b)  v  (c)  v  (d)  v 
 4 
 3 
 3 
 4 
 7 
 4 
 7 
 3 
 Q.8.  A  vessel  is  ?lled  with  liquid,  5  parts 
 of  which  are  water  and  11  parts  syrup. 
 What  part  of  the  mixture  must  be  drawn 
 off  and  replaced  with  water  so  that  the 
 mixture  may  be  syrup  and  water  in  the 
 ratio 3 : 2 ? 
 SSC CGL 26/07/2023 (1st shift) 
 (a)  (b)  (c)  (d) 
 14 
 45 
 27 
 35 
 36 
 65 
 7 
 55 
 Q.9.  Alloy  X  contains  70%  copper  and 
 30%  zinc.  Alloy  Y  contains  40%  copper, 
 25%  zinc  and  35%  aluminum.  Alloy  X  and 
 Y  are  mixed  in  the  ratio  of  1  :  3.  What  is 
 the  ratio  of  copper  and  zinc  in  the  newly 
 formed alloy ? 
 SSC MTS 17/05/2023 (Afternoon) 
 (a) 19 : 33  (b) 11 : 32 
 (c) 38 : 21  (d) 19 : 21 
 Q.10.  A  jar  contains  a  mixture  of  milk 
 and  water,  having  50%  water.  A  part  of 
 this  mixture  is  replaced  by  another 
 mixture  having  29%  water.  The 
 percentage  of  water  in  the  jar  after 
 replacement  is  36%.  What  fraction  of  the 
 original mixture was replaced ? 
 SSC MTS 10/05/2023 (Afternoon) 
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 Pinnacle  Day: 54th  Mixture and Alligation 
 (a)  (b)  (c)  (d) 
 3 
 2 
 4 
 5 
 1 
 3 
 2 
 3 
 Q.11.  A  100  ml  solution  of  having  ?? 
 2 
 ???? 
 4 
 concentration  of  20%  is  mixed  with  a 
 50%  concentrated  x  ml  mixture  such  that 
 the  net  mixture  is  30%  concentrated. 
 Determine x. 
 SSC CGL  08/12/2022 (1st Shift) 
 (a) 70 ml  (b) 80 ml  (c) 60 ml  (d) 50 ml 
 Q.12.  The  cost  of  two  varieties  of  tea  is 
 ?300  and  ?375  respectively.  If  both  the 
 varieties  of  tea  are  mixed  together  in  the 
 ratio  3  :  2,  then  what  should  be  the  price 
 of the mixed variety of tea per kg? 
 SSC CPO 09/11/2022 (Morning) 
 (a) ?340 (b) ?330 (c) ?350 (d) ?360 
 Q.13.  Two  vessels  of  equal  capacity,  and 
 both  completely  ?lled,  contain  mixtures 
 of  milk  and  water  in  the  ratio  5  :  1  and  6  : 
 5,  respectively.  Both  the  mixtures  are 
 now  mixed  thoroughly.  What  is  the  ratio 
 of  milk  to  water  in  the  new  mixture  so 
 obtained? 
 SSC MTS 13/07/2022 (Evening) 
 (a) 105 : 67  (b) 57 : 41 
 (c) 91 : 41  (d) 28 : 43 
 Q.14.  Babulal  runs  a  juice  corner  outside 
 a  park  and  sells  giloy  juice  (giloy  +  water) 
 in  the  morning.  Initially  he  had  19  litres  of 
 juice,  which  had  giloy  and  water  in  the 
 ratio  2  :  9.  He  sold  2  litres  of  juice. 
 1 
 2 
 Later,  in  order  to  dilute  it,  he  added  some 
 water  and  the  ratio  of  giloy  and  water 
 became  1  :  5.  How  much  water  was 
 added ? 
 SSC MTS 27/10/2021 (Morning) 
 (a) 1  litres  (b)  litre 
 1 
 2 
 1 
 2 
 (c)  2 litres  (d) 1 litre 
 Q.15.  Alloy  A  contains  metal  x  and  y  only 
 in  the  ratio  5  :  2  and  alloy  B  contains 
 these  metals  in  the  ratio  3  :  4.  Alloy  C  is 
 prepared by mixing A and B in the ratio 
 4 : 5. The percentage of x in alloy C is: 
 SSC CGL Tier II (16/11/2020) 
 (a) 44  (b) 56  (c) 45  (d) 55 
 4 
 9 
 5 
 9 
 Q.16.  Two  bottles  of  same  capacity  are 
 35%  and  33  %  full  of  orange  juice, 
 1 
 3 
 respectively.  They  are  ?lled  up 
 completely  with  apple  juice  and  then  the 
 contents  of  both  bottles  are  emptied  into 
 another  vessel.  The  percentage  of  apple 
 juice in the mixture is: 
 SSC CGL 03/03/2020 (Afternoon) 
 (a) 34  (b) 64  (c) 60  (d) 65 
 1 
 6 
 1 
 3 
 2 
 3 
 5 
 6 
 Q.17.  A  vessel  contains  a  32  litre 
 solution  of  acid  and  water  in  which  the 
 ratio  of  acid  and  water  is  5  :  3.  If  12  litres 
 of  the  solution  are  taken  out  and  7 
 1 
 2 
 litres  of  water  are  added  to  it,  then  what 
 is  the  ratio  of  acid  and  water  in  the 
 resulting solution ? 
 SSC CGL Tier II (13/09/2019) 
 (a) 4 : 7  (b) 5 : 6  (c) 4 : 9  (d) 8 : 11 
 Q.18.  The  ratios  of  copper  to  Zinc  in  alloys 
 A  and  B  are  3  :  4  and  5  :  9  respectively.  A 
 and  B  are  taken  in  the  ratio  2:3  and  melted 
 to  form  a  new  alloy  C.  What  is  the  ratio  of 
 copper to Zinc in C ? 
 SSC CGL Tier II (11/09/2019) 
 (a) 8 : 13  (b) 3 : 5  (c) 9 : 11  (d) 27 : 43 
 Q.19.  A  mixture  contains  milk  and  water 
 in  the  ratio  (by  volume)  5  :  3  and  another 
 mixture,  of  the  same  volume  as  that  of 
 the  former,  contains  water  and  milk  in  the 
 ratio  (by  volume)  1  :  3.  In  what  ratio,  two 
 mixture  be  mixed  in  order  to  obtain  a  new 
 mixture  consisting  of  milk  and  water  in 
 the ratio (by volume) 7 : 3 ? 
 SSC MTS 13/08/2019 (Afternoon) 
 (a) 2 : 3  (b) 3 : 4  (c) 5 : 6  (d) 3 : 2 
 Q.20.  In  the  60  litre  mixture  of  milk  and 
 water,  the  quantities  of  milk  and  water 
 are  in  the  ratio  of  3  :  2.  If  we  want  to 
 make  the  ratio  of  the  quantities  of  milk 
 and  water  1  :  1,  then  how  much  extra 
 water should be put in the mixture ? 
 SSC MTS 05/08/2019 (Afternoon) 
 (a)10 litre (b) 16litre  (c)12 litre (d)14 litre 
 Q.21.  A  milkman  uses  three  containers 
 for  selling  milk,  their  capacities  being 
 40L,  30L  and  20L  respectively.  He  ?lls 
 respectively  87.5%,  80%  and  90%  of  the 
 containers  with  a  mix  of  milk  and  water 
 in  the  ratios,  3  :  2,  5  :  1  and  7  :  2 
 respectively.  What  is  the  ratio  of  total 
 quantity  of  milk  to  that  of  water  carried 
 by him ? 
 SSC CHSL 10/07/2019 (Evening) 
 (a) 7 : 2  (b) 31 : 12   (c) 35 : 9   (d) 5 : 2 
 Q.22.  Fresh  fruit  contains  68%  water  and 
 dry  fruit  contains  20%  water.  How  much 
 dry  fruit  can  be  obtained  from  100  kg  of 
 fresh fruit 
 SSC CPO 16/03/2019 (Morning) 
 (a) 80  (b) 60  (c) 40  (d) 20 
 Practice Questions 
 SSC CPO 2023 Tier - 1 
 Q.23.  If 60 liters of a milk solution has 
 40% milk in it, then how much milk 
 should  be  added  to  make  the  milk  60%  in 
 the solution? 
 SSC CPO 03/10/2023 (3rd Shift) 
 (a) 30 liters  (b) 20 liters 
 (c) 35 liters  (d) 25 liters 
 Q.24.  Two  mixtures  A  and  B  have  the 
 following compositions: 
 Mixture  A  has  copper  and  tin  in  a  ratio  of 
 1 : 2 
 Mixture  B  has  copper  and  tin  in  a  ratio  of 
 1 : 3 
 If  equal  quantities  of  mixtures  A  and  B 
 are  used  for  producing  mixture  C,  then 
 ?nd  the  ratio  of  copper  and  tin  in  mixture 
 C. 
 SSC CPO 04/10/2023 (3rd Shift) 
 (a) 2 : 5    (b) 7 : 17    (c) 7 : 12    (d) 1 : 5 
 SSC MTS 2023 Tier -1 
 Q.25.  There  is  a  25  litre  mixture  of  milk 
 and  water,  containing  milk  and  water  in 
 the  ratio  3  :  2.  Find  the  number  of  litres  of 
 water  that  should  be  added  to  the 
 mixture  so  that  the  resultant  mixture  has 
 50% water in it. 
 SSC MTS 01/09/2023 (2nd Shift) 
 (a) 10  (b) 8  (c) 5  (d) 12 
 Q.26.  From  a  container  having  pure  milk, 
 35%  is  replaced  by  water  and  the  process 
 is  repeated  thrice.  At  the  end  of  the  third 
 operation, the purity of the milk is: 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 21  %  (b) 37  % 
 23 
 80 
 21 
 80 
 (c) 23  %  (d) 27  % 
 37 
 80 
 37 
 80 
 Q.27.  In  what  ratio  must  a  grocer  mix  two 
 varieties  of  pulses  costing  ?18  per  kg 
 and  ?22  per  kg,  respectively,  so  as  to  get 
 a mixture worth ?19.50 per kg? 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 5 : 3  (b) 5 : 1  (c) 1 : 5  (d) 5 : 2 
 Q.28.  How  many  kilograms  of  sugar  at 
 ?3.80  per  kg  must  be  mixed  with  60  kg  of 
 sugar  at  ?4.60  per  kg,  so  that  by  selling 
 the  mixture  at  ?5.20  per  kg  there  may  be 
 a gain of 30%? 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 170 kg  (b) 120 kg  (c) 160 kg (d) 180 kg 
 Q.29.  A  mixture  contains  milk  and  water 
 in  the  ratio  9  :  7.  If  it  contains  4  litres 
 more  milk  than  water,  then  ?nd  the 
 quantity of milk (in litres) in the mixture. 
 SSC MTS 04/09/2023 (1st Shift) 
 (a) 18  (b) 15  (c) 21  (d) 14 
 Q.30.  A  vessel  contains  liquid  A  and 
 liquid  B  in  the  ratio  4  :  9.  If  8  litres  of 
 liquid  A  is  added  to  the  vessel,  the  new 
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 Pinnacle  Day: 54th  Mixture and Alligation 
 ratio  becomes  8  :  9.  Find  the  quantity  of 
 liquid A (in litres) in the original mixture. 
 SSC MTS 04/09/2023 (2nd Shift) 
 (a) 12  (b) 9  (c) 8  (d) 6 
 Q.31.  If  two  varieties  of  a  grain  worth 
 ?202  per  kg  and  ?250  per  kg, 
 respectively,  are  mixed  in  the  ratio  of  7  : 
 5,  then  what  is  the  cost  (in  ?)  of  the 
 resulting mixture per kg? 
 SSC MTS 05/09/2023 (1st Shift) 
 (a) 225  (b) 218  (c) 222  (d) 220 
 Q.32.  Two  containers  of  equal  capacity 
 are  full  of  a  mixture  of  milk  and  water.  In 
 the  ?rst  container,  the  ratio  of  milk  to 
 water  is  3  :11  and  in  the  second 
 container  the  ratio  is  9  :11.  If  both  the 
 mixtures  are  mixed  in  a  container,  what  is 
 the resulting ratio of milk to water? 
 SSC MTS 06/09/2023 (2nd Shift) 
 (a) 87 : 197  (b) 21 : 87 
 (c) 93 : 187  (d) 93 : 179 
 Q.33.  There  are  two  varieties  of  rice. 
 Variety  1  costs  ?100  per  kg  and  variety  2 
 costs  ?120  per  kg.  The  vendor  mixed 
 both  the  varieties  and  sold  for  ?121  per 
 kg  and  gained  10%.  Find  the  ratio  of 
 variety 1 to variety 2 rice in the mixture. 
 SSC MTS 08/09/2023 (1st Shift) 
 (a) 1 : 1  (b) 3 : 1  (c) 2 : 1  (d) 1 : 3 
 Q.34.  Tea  leaves  worth  ?108  per  kg  and 
 ?120  per  kg  are  mixed  with  a  third  variety 
 in  the  ratio  2  :  3  :  5.  If  the  mixture  is  worth 
 ?125  per  kg,  the  price  (in  ?,  rounded  off 
 to  the  nearest  integer)  of  the  third  variety 
 of tea leaves per kg will be: 
 SSC MTS 08/09/2023 (3rd Shift) 
 (a) 130  (b) 128  (c) 135  (d) 133 
 Q.35.  In  some  quantity  of  water,four 
 times  the  quantity  of  milk  is  added  and 
 the  quantity  of  the  mixture  is  now  7.5 
 litres.  How  much  more  milk  is  to  be 
 added  to  the  mixture  to  have  90%  milk  in 
 the mixture ? 
 SSC MTS 11/09/2023 (1st Shift) 
 (a) 9 liters  (b) 9.5 liters 
 (c) 6 liters  (d) 7.5 liters 
 Q.36.  15  kg  of  ?25  per  kg  wheat  is  mixed 
 with  10  kg  of  another  type  of  wheat  to 
 get  a  mixture  costing  ?30  per  kg.  Find  the 
 price (per kg) of the costlier wheat. 
 SSC MTS 13/09/2023 (1st Shift) 
 (a) ?37.5  (b) ?32.5  (c) ?35.5  (d) ?30.5 
 Q.37.  A  mixture  contains  spirit  and  water 
 in  the  ratio  3  :  2.  If  2  litres  of  water  is 
 added  to  the  mixture,  the  ratio  becomes 
 5  :  4,  Find  the  quantity  of  spirit  in  the 
 mixture (in litres). 
 SSC MTS 13/09/2023 (2nd Shift) 
 (a) 15  (b) 20  (c) 25  (d) 10 
 Q.38.  In  what  ratio  should  rice  worth 
 ?140  per  kg  and  ?90  per  kg  be  mixed  so 
 that  a  mixture  of  two  qualities  of  rice 
 may become worth  ?110 per kg? 
 SSC MTS 14/09/2023 (3rd Shift) 
 (a) 2 : 3  (b) 1 : 3   (c) 3 : 2  (d) 1 : 2 
 SSC CHSL 2023 Tier - 1 
 Q.39.  A bottle is ?lled with liquid of which 
 4  parts  are  water  and  5  parts  are  fruit 
 extract.  How  much  of  the  mixture  must 
 be  drawn  off  and  replaced  with  water  so 
 that  the  mixture  may  be  half  water  and 
 half fruit extract ? 
 SSC CHSL 03/08/2023 (3rd Shift) 
 (a)  (b)  (c)  (d) 
 1 
 10 
 9 
 10 
 4 
 9 
 5 
 9 
 Q.40.  How  much  chicory,  costing 
 ?100/kg  should  be  added  to  40  kg  of 
 coffee  costing  ?45/kg  so  that  the  mixture 
 will be worth ?60/kg ? 
 SSC CHSL 03/08/2023 (3rd Shift) 
 (a) 12.5 kg (b) 5 kg (c) 17.5 kg (d) 15 kg 
 Q.41.  Milk  and  water  in  two  vessels  A 
 and  B  are  in  the  ratio  5  :  3  and  2  :  3, 
 respectively.  In  what  ratio  should  the 
 liquids  in  both  the  vessels  be  mixed  to 
 obtain  a  new  mixture  in  vessel  C 
 containing half milk and half water ? 
 SSC CHSL 04/08/2023 (1st Shift) 
 (a) 3 : 4  (b) 4 : 5  (c) 2 : 3   (d) 3 : 5 
 Q.42.  In  two  alloys,  the  ratio  of 
 Aluminium  to  Zinc  are  5  :  6  and  3  :  5.  If 
 242  kg  of  the  ?rst  alloy  and  144  kg  of  the 
 second  alloy  are  mixed,  then  the  ratio  of 
 Aluminium  and  Zinc  in  the  new  alloy  will 
 be: 
 SSC CHSL 07/08/2023 (4th Shift) 
 (a) 76 : 117  (b) 82 : 111 
 (c) 93 : 100  (d) 68 : 125 
 Q.43.  In  what  ratio  does  a  grocer  mix  tea 
 at  ?26  per  kg  and  ?32  per  kg  so  that  by 
 selling  the  mixture  at  ?30  per  kg  they 
 may gain 10%. ? 
 SSC CHSL 08/08/2023 (2nd Shift) 
 (a) 7 : 26  (b) 16 : 7   (c) 26 : 7   (d) 7 : 16 
 Q.44.  In  what  ratio,  wheat  at  ?23  per  kg 
 should  be  mixed  with  wheat  at  ?  14  per 
 kg  so  that  on  selling  the  mixture  at  ?  20 
 per kg there is a pro?t of 25% ? 
 SSC CHSL 09/08/2023 (1st Shift) 
 (a) 5 : 7    (b) 3 : 5     (c) 2 : 3    (d) 2 : 7 
 Q.45.  One  litre  milk  costs  ?40.  Water  is 
 mixed  with  milk  and  the  mixture  was  sold 
 at  ?30  per  litre.  Find  the  ratio  of  water 
 and milk in the mixture 
 SSC CHSL 09/08/2023 (3rd Shift) 
 (a)  2 : 5   (b)  1 : 3   (c)  1 : 2   (d)  2 : 3 
 Q.46.  In  a  mixture  of  178  litres,  the  ratio 
 of  water  and  milk  is  5  :  7.  How  much 
 water should be added to make the ratio 
 of water and milk 3 : 4 ? 
 SSC CHSL 10/08/2023 (1st Shift) 
 (a) 3  liters  (b)  liters 
 17 
 24 
 3 
 13 
 24 
 (c) 2  liters  (d) 2  liters 
 11 
 24 
 23 
 24 
 Q.47.  In  a  mixture,  the  ratio  of  a  chemical 
 X  and  water  is  15  :  9.  When  48  litres  of 
 this  mixture  is  replaced  with  water,  the 
 ratio  becomes  11  :  13.  Find  the  quantity 
 of water after replacement. 
 SSC CHSL 10/08/2023 (2nd Shift) 
 (a) 97.5 litres  (b) 99 litres 
 (c) 92 litres  (d) 102.5 litres 
 Q.48.  A  grocer  mixes  two  varieties  of  tea 
 priced  at  ?80  kg  and  ?85/kg  in  a  certain 
 ratio  to  produce  a  new  variety  priced  at 
 ?82/kg.  What  is  the  ratio  in  which  the  two 
 varieties  were  mixed  to  obtain  the  new 
 variety ? 
 SSC CHSL 10/08/2023 (3rd Shift) 
 (a) 1 : 3   (b) 2 : 5   (c) 4 : 4   (d) 3 : 2 
 Q.49.  Rice  worth  ?504  per  kg  and  ?540 
 per  kg  are  mixed  with  the  third  variety  in 
 the  ratio  1  :  1  :  2.  If  the  mixture  is  worth 
 ?612  per  kg,  ?nd  the  price  (per  kg  in  ?)  of 
 the third variety. 
 SSC CHSL 10/08/2023 (4th Shift) 
 (a) 630  (b) 702  (c) 764  (d) 522 
 Q.50.  How  many  kilograms  of  rice 
 costing  ?52  per  kg  must  be  mixed  with 
 35  kg  of  rice  costing  ?45  per  kg  so  as  to 
 get  a  gain  of  10%  by  selling  the  resulting 
 mixture of rice at the rate of ?55 per kg ? 
 SSC CHSL 11/08/2023 (2nd Shift) 
 (a) 87.5 kg  (b) 90.0 kg 
 (c) 85.0 kg  (d) 82.5 kg 
 Q.51.  In  an  experiment,  it  was  observed 
 that  metal  A  is  19  times  heavier  than 
 water  and  metal  B  is  9  times  heavier  than 
 water.  In  what  ratio  metal  A  and  B  mixed 
 so  that  the  mixture  thus  obtained  be  15 
 times heavier than water ? 
 SSC CHSL 11/08/2023 (3rd Shift) 
 (a) 2 : 3   (b) 1 : 3   (c) 3 : 1   (d) 3 : 2 
 Q.52.  Two  jars  A  and  B  are  containing 
 the  solutions  of  two  liquids  P  and  Q  .  The 
 ratio  of  the  liquids  P  and  Q  in  the  jars  A 
 and  B  are  2:  19  and  1:  11,  respectively.  If 
 7  litres  of  the  solution  of  jar  A  and  4  litres 
 of  the  solution  of  jar  B  are  mixed,  what  is 
 the  ratio  of  the  solutions  P  and  Q  in  the 
 new mixture ? 
 SSC CHSL 11/08/2023 (4th Shift) 
 (a) 10 : 1    (b) 1 : 9   (c) 9 : 1   (d) 1 : 10 
 Q.53.  If two qualities of a fruit costing 
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Page 4


 Pinnacle  Day: 54th  Mixture and Alligation 
 Mixture and Alligation 
 Mixture  :  when  two  or  more  than  two 
 substances  mixed  together  in  any  ratio  to 
 produce a product is called mixture . 
 Mean  price  :  the  average  of  all  the  given 
 prices  of  the  known  items  is  called  Mean 
 Price . 
 1.  Alligation  rule  :  It  is  used  to  ?nd  the 
 ratio  in  which  two  or  more  substances  at 
 their  respective  prices  should  be  mixed 
 to produce a mixture at a given price. 
 where 
 C = Cost price of cheaper 
 D = Cost price of dearer 
 M = Mean price 
 (D - M) = Cheaper quantity 
 (M - C) = Dearer quantity 
 2. Quantity of pure liquid  =  ?? (
 ??    -    ?? 
 ?? 
)
 ?? 
 where,  =  Quantity  of  original  liquid,  =  ??  ?? 
 Quantity  to  be  carried  out  and  replaced,  ?? 
 =  Number  of  times  the  operation  is 
 conducted 
 Important Cases :- 
 Case 1  : 
 Ratio  of  milk  and  water  in  container  A,  B 
 and  C  are  1  :  2,  4  :  1  and  4  :  5 
 respectively.  Find  the  ratio  in  which 
 containers  A  and  B  are  mixed  to  get  4  :  5 
 in container C ? 
 Soln :  Fraction of milk in container A = 
 1 
 3 
 Fraction of milk in container B = 
 4 
 5 
 Fraction of milk in container C = 
 4 
 9 
 So, the required ratio = 16 : 5 
 Case 2  : 
 Ratio  of  milk  and  water  in  container  A 
 and  B  are  3  :  1  and  4  :  1  respectively. 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  Find  the  ratio  of 
 quantity of milk and water in container C. 
 Soln : 
 Fraction of milk in container A = 
 3 
 4 
 Fraction of milk in container B = 
 4 
 5 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  So,  let  the  quantity  in 
 container  A  and  B  be  2  litre  and  1  litre 
 respectively. 
 So, the required ratio = 
 [  2  ]  +  [  1] : [  2]  +  [  1] 
 3 
 4 
×
 4 
 5 
×
 1 
 4 
×
 1 
 5 
×
 =  +  :  +  =  :  = 23 : 7 
 3 
 2 
 4 
 5 
 1 
 2 
 1 
 5 
 23 
 10 
 7 
 10 
 Case  3  :  Two  varieties  costing  ?4/kg  and 
 ?5/kg  respectively  are  mixed  in  3  :  2.  Find 
 the  cost  price  per  kg  of  the  resultant 
 mixture? 
 Soln: 
 A 
 wt 
 =  = 
 ??  1  ??  1    +    ??  2  ??  2 
 ??  1    +    ??  2 
 4     ×     3    +    5     ×     2 
 3    +    2 
 =  =  = 4.4 kg 
 12    +    10 
 5 
 22 
 5 
 Variety Questions 
 Q.1.  80  litres  of  a  mixture  of  spirit  and 
 water  in  the  ratio  7  :  9  is  present  in  a 
 container  A.  20  litres  of  the  mixture  is 
 transferred  to  another  container  B.  Then 
 the  container  A  is  ?lled  with  20  litres  of 
 water.  Then  32  litres  of  the  mixture  is 
 again  transferred  to  container  B.  The 
 ratio  of  water  to  spirit  of  the  mixture  in 
 container B is equal to: 
 SSC CGL Tier II  (26/10/2023) 
 (a) 41 : 87  (b) 87 : 41 
 (c) 131 : 77  (d) 77 : 131 
 Q.2.  At  a  certain  time  in  a  park,  the 
 number  of  heads  and  the  number  of  legs 
 of  monkeys  and  human  visitors  were 
 counted,  and  it  was  found  that  there  were 
 54  heads  and  148  legs.  Find  the  number 
 of monkeys in the park. 
 SSC CGL Tier II  (26/10/2023) 
 (a) 20  (b) 16  (c) 18  (d) 14 
 Q.3.  A  milk  vendor  has  2  vessels  of  milk 
 and  water.  The  ?rst  contains  80%  milk 
 and  the  rest  is  water.  The  second 
 contains  50%  milk.  How  much  mixture  (in 
 L)  should  he  mix  from  each  of  the 
 vessels  so  as  to  get  9  litres  of  mixture 
 such  that  the  ratio  of  water  to  milk  is  1  :  2 
 ?  (Write  your  answer  in  the  order  of 
 vessel 1 and vessel 2) 
 SSC MTS 13/09/2023 (1st Shift) 
 (a) 6, 3  (b) 4, 5  (c) 3, 6  (d) 5, 4 
 Q.4.  A  blended  tea  in  a  barrel  contains 
 Assam,  Darjeeling  and  Nilgiri  Hills  in  the 
 ratio  2  :  3  :  1.  Another  barrel  contains 
 Darjeeling,  Nilgiri  Hills  and  Kangra  Valley 
 in  the  ratio  5  :  4  :  3.  If  equal  weights  of 
 both  blended  tea  mix  together  to  make  a 
 new brand, then the weight of Kangra 
 Valley per kilogram in the new brand is: 
 SSC CHSL 10/08/2023 (3rd Shift) 
 (a) 500 gm  (b) 100 gm 
 (c) 250 gm  (d) 125 gm 
 Q.5.  From  a  cask  of  milk  containing  64 
 liters,  8  liters  are  drawn  out  and  the  cask 
 is  ?lled  up  with  water.  If  the  same 
 process  is  repeated  a  second,  then  a 
 third  time,  what  will  be  the  proportion  of 
 milk to water in the resulting mixture ? 
 SSC CHSL 09/08/2023 (2nd Shift) 
 (a) 343 : 179  (b) 333 : 169 
 (c) 443 : 179  (d) 343 : 169 
 Q.6.  A  jar  contains  35%  syrup  in  the 
 mixture  of  syrup  and  water.  A  part  of  this 
 mixture  is  replaced  by  another  mixture 
 containing  20%  syrup.  Now,  in  the  new 
 mixture,  the  percentage  of  syrup  is  found 
 to  be  24%.  What  is  the  ratio  in  which 
 these  mixtures  were  mixed  to  obtain  the 
 new mixture ? 
 SSC CHSL 07/08/2023 (2nd Shift) 
 (a) 3 : 14  (b) 4 : 11  (c) 5 : 13  (d) 7 : 10 
 Q.7.  In  a  solution  of  water  and  milk,  the 
 quantity  of  milk  is  double  the  quantity  of 
 water.  To  pass  the  quality  standards,  the 
 solution  must  contain  90%  milk  in  it.  If 
 the  volume  of  the  solution  is  v,  then  how 
 much  pure  milk  in  litres  is  to  be  added  to 
 the solution to pass the quality standard. 
 SSC CHSL 02/08/2023 (2nd Shift) 
 (a)  v  (b)  v  (c)  v  (d)  v 
 4 
 3 
 3 
 4 
 7 
 4 
 7 
 3 
 Q.8.  A  vessel  is  ?lled  with  liquid,  5  parts 
 of  which  are  water  and  11  parts  syrup. 
 What  part  of  the  mixture  must  be  drawn 
 off  and  replaced  with  water  so  that  the 
 mixture  may  be  syrup  and  water  in  the 
 ratio 3 : 2 ? 
 SSC CGL 26/07/2023 (1st shift) 
 (a)  (b)  (c)  (d) 
 14 
 45 
 27 
 35 
 36 
 65 
 7 
 55 
 Q.9.  Alloy  X  contains  70%  copper  and 
 30%  zinc.  Alloy  Y  contains  40%  copper, 
 25%  zinc  and  35%  aluminum.  Alloy  X  and 
 Y  are  mixed  in  the  ratio  of  1  :  3.  What  is 
 the  ratio  of  copper  and  zinc  in  the  newly 
 formed alloy ? 
 SSC MTS 17/05/2023 (Afternoon) 
 (a) 19 : 33  (b) 11 : 32 
 (c) 38 : 21  (d) 19 : 21 
 Q.10.  A  jar  contains  a  mixture  of  milk 
 and  water,  having  50%  water.  A  part  of 
 this  mixture  is  replaced  by  another 
 mixture  having  29%  water.  The 
 percentage  of  water  in  the  jar  after 
 replacement  is  36%.  What  fraction  of  the 
 original mixture was replaced ? 
 SSC MTS 10/05/2023 (Afternoon) 
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 Pinnacle  Day: 54th  Mixture and Alligation 
 (a)  (b)  (c)  (d) 
 3 
 2 
 4 
 5 
 1 
 3 
 2 
 3 
 Q.11.  A  100  ml  solution  of  having  ?? 
 2 
 ???? 
 4 
 concentration  of  20%  is  mixed  with  a 
 50%  concentrated  x  ml  mixture  such  that 
 the  net  mixture  is  30%  concentrated. 
 Determine x. 
 SSC CGL  08/12/2022 (1st Shift) 
 (a) 70 ml  (b) 80 ml  (c) 60 ml  (d) 50 ml 
 Q.12.  The  cost  of  two  varieties  of  tea  is 
 ?300  and  ?375  respectively.  If  both  the 
 varieties  of  tea  are  mixed  together  in  the 
 ratio  3  :  2,  then  what  should  be  the  price 
 of the mixed variety of tea per kg? 
 SSC CPO 09/11/2022 (Morning) 
 (a) ?340 (b) ?330 (c) ?350 (d) ?360 
 Q.13.  Two  vessels  of  equal  capacity,  and 
 both  completely  ?lled,  contain  mixtures 
 of  milk  and  water  in  the  ratio  5  :  1  and  6  : 
 5,  respectively.  Both  the  mixtures  are 
 now  mixed  thoroughly.  What  is  the  ratio 
 of  milk  to  water  in  the  new  mixture  so 
 obtained? 
 SSC MTS 13/07/2022 (Evening) 
 (a) 105 : 67  (b) 57 : 41 
 (c) 91 : 41  (d) 28 : 43 
 Q.14.  Babulal  runs  a  juice  corner  outside 
 a  park  and  sells  giloy  juice  (giloy  +  water) 
 in  the  morning.  Initially  he  had  19  litres  of 
 juice,  which  had  giloy  and  water  in  the 
 ratio  2  :  9.  He  sold  2  litres  of  juice. 
 1 
 2 
 Later,  in  order  to  dilute  it,  he  added  some 
 water  and  the  ratio  of  giloy  and  water 
 became  1  :  5.  How  much  water  was 
 added ? 
 SSC MTS 27/10/2021 (Morning) 
 (a) 1  litres  (b)  litre 
 1 
 2 
 1 
 2 
 (c)  2 litres  (d) 1 litre 
 Q.15.  Alloy  A  contains  metal  x  and  y  only 
 in  the  ratio  5  :  2  and  alloy  B  contains 
 these  metals  in  the  ratio  3  :  4.  Alloy  C  is 
 prepared by mixing A and B in the ratio 
 4 : 5. The percentage of x in alloy C is: 
 SSC CGL Tier II (16/11/2020) 
 (a) 44  (b) 56  (c) 45  (d) 55 
 4 
 9 
 5 
 9 
 Q.16.  Two  bottles  of  same  capacity  are 
 35%  and  33  %  full  of  orange  juice, 
 1 
 3 
 respectively.  They  are  ?lled  up 
 completely  with  apple  juice  and  then  the 
 contents  of  both  bottles  are  emptied  into 
 another  vessel.  The  percentage  of  apple 
 juice in the mixture is: 
 SSC CGL 03/03/2020 (Afternoon) 
 (a) 34  (b) 64  (c) 60  (d) 65 
 1 
 6 
 1 
 3 
 2 
 3 
 5 
 6 
 Q.17.  A  vessel  contains  a  32  litre 
 solution  of  acid  and  water  in  which  the 
 ratio  of  acid  and  water  is  5  :  3.  If  12  litres 
 of  the  solution  are  taken  out  and  7 
 1 
 2 
 litres  of  water  are  added  to  it,  then  what 
 is  the  ratio  of  acid  and  water  in  the 
 resulting solution ? 
 SSC CGL Tier II (13/09/2019) 
 (a) 4 : 7  (b) 5 : 6  (c) 4 : 9  (d) 8 : 11 
 Q.18.  The  ratios  of  copper  to  Zinc  in  alloys 
 A  and  B  are  3  :  4  and  5  :  9  respectively.  A 
 and  B  are  taken  in  the  ratio  2:3  and  melted 
 to  form  a  new  alloy  C.  What  is  the  ratio  of 
 copper to Zinc in C ? 
 SSC CGL Tier II (11/09/2019) 
 (a) 8 : 13  (b) 3 : 5  (c) 9 : 11  (d) 27 : 43 
 Q.19.  A  mixture  contains  milk  and  water 
 in  the  ratio  (by  volume)  5  :  3  and  another 
 mixture,  of  the  same  volume  as  that  of 
 the  former,  contains  water  and  milk  in  the 
 ratio  (by  volume)  1  :  3.  In  what  ratio,  two 
 mixture  be  mixed  in  order  to  obtain  a  new 
 mixture  consisting  of  milk  and  water  in 
 the ratio (by volume) 7 : 3 ? 
 SSC MTS 13/08/2019 (Afternoon) 
 (a) 2 : 3  (b) 3 : 4  (c) 5 : 6  (d) 3 : 2 
 Q.20.  In  the  60  litre  mixture  of  milk  and 
 water,  the  quantities  of  milk  and  water 
 are  in  the  ratio  of  3  :  2.  If  we  want  to 
 make  the  ratio  of  the  quantities  of  milk 
 and  water  1  :  1,  then  how  much  extra 
 water should be put in the mixture ? 
 SSC MTS 05/08/2019 (Afternoon) 
 (a)10 litre (b) 16litre  (c)12 litre (d)14 litre 
 Q.21.  A  milkman  uses  three  containers 
 for  selling  milk,  their  capacities  being 
 40L,  30L  and  20L  respectively.  He  ?lls 
 respectively  87.5%,  80%  and  90%  of  the 
 containers  with  a  mix  of  milk  and  water 
 in  the  ratios,  3  :  2,  5  :  1  and  7  :  2 
 respectively.  What  is  the  ratio  of  total 
 quantity  of  milk  to  that  of  water  carried 
 by him ? 
 SSC CHSL 10/07/2019 (Evening) 
 (a) 7 : 2  (b) 31 : 12   (c) 35 : 9   (d) 5 : 2 
 Q.22.  Fresh  fruit  contains  68%  water  and 
 dry  fruit  contains  20%  water.  How  much 
 dry  fruit  can  be  obtained  from  100  kg  of 
 fresh fruit 
 SSC CPO 16/03/2019 (Morning) 
 (a) 80  (b) 60  (c) 40  (d) 20 
 Practice Questions 
 SSC CPO 2023 Tier - 1 
 Q.23.  If 60 liters of a milk solution has 
 40% milk in it, then how much milk 
 should  be  added  to  make  the  milk  60%  in 
 the solution? 
 SSC CPO 03/10/2023 (3rd Shift) 
 (a) 30 liters  (b) 20 liters 
 (c) 35 liters  (d) 25 liters 
 Q.24.  Two  mixtures  A  and  B  have  the 
 following compositions: 
 Mixture  A  has  copper  and  tin  in  a  ratio  of 
 1 : 2 
 Mixture  B  has  copper  and  tin  in  a  ratio  of 
 1 : 3 
 If  equal  quantities  of  mixtures  A  and  B 
 are  used  for  producing  mixture  C,  then 
 ?nd  the  ratio  of  copper  and  tin  in  mixture 
 C. 
 SSC CPO 04/10/2023 (3rd Shift) 
 (a) 2 : 5    (b) 7 : 17    (c) 7 : 12    (d) 1 : 5 
 SSC MTS 2023 Tier -1 
 Q.25.  There  is  a  25  litre  mixture  of  milk 
 and  water,  containing  milk  and  water  in 
 the  ratio  3  :  2.  Find  the  number  of  litres  of 
 water  that  should  be  added  to  the 
 mixture  so  that  the  resultant  mixture  has 
 50% water in it. 
 SSC MTS 01/09/2023 (2nd Shift) 
 (a) 10  (b) 8  (c) 5  (d) 12 
 Q.26.  From  a  container  having  pure  milk, 
 35%  is  replaced  by  water  and  the  process 
 is  repeated  thrice.  At  the  end  of  the  third 
 operation, the purity of the milk is: 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 21  %  (b) 37  % 
 23 
 80 
 21 
 80 
 (c) 23  %  (d) 27  % 
 37 
 80 
 37 
 80 
 Q.27.  In  what  ratio  must  a  grocer  mix  two 
 varieties  of  pulses  costing  ?18  per  kg 
 and  ?22  per  kg,  respectively,  so  as  to  get 
 a mixture worth ?19.50 per kg? 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 5 : 3  (b) 5 : 1  (c) 1 : 5  (d) 5 : 2 
 Q.28.  How  many  kilograms  of  sugar  at 
 ?3.80  per  kg  must  be  mixed  with  60  kg  of 
 sugar  at  ?4.60  per  kg,  so  that  by  selling 
 the  mixture  at  ?5.20  per  kg  there  may  be 
 a gain of 30%? 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 170 kg  (b) 120 kg  (c) 160 kg (d) 180 kg 
 Q.29.  A  mixture  contains  milk  and  water 
 in  the  ratio  9  :  7.  If  it  contains  4  litres 
 more  milk  than  water,  then  ?nd  the 
 quantity of milk (in litres) in the mixture. 
 SSC MTS 04/09/2023 (1st Shift) 
 (a) 18  (b) 15  (c) 21  (d) 14 
 Q.30.  A  vessel  contains  liquid  A  and 
 liquid  B  in  the  ratio  4  :  9.  If  8  litres  of 
 liquid  A  is  added  to  the  vessel,  the  new 
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 Pinnacle  Day: 54th  Mixture and Alligation 
 ratio  becomes  8  :  9.  Find  the  quantity  of 
 liquid A (in litres) in the original mixture. 
 SSC MTS 04/09/2023 (2nd Shift) 
 (a) 12  (b) 9  (c) 8  (d) 6 
 Q.31.  If  two  varieties  of  a  grain  worth 
 ?202  per  kg  and  ?250  per  kg, 
 respectively,  are  mixed  in  the  ratio  of  7  : 
 5,  then  what  is  the  cost  (in  ?)  of  the 
 resulting mixture per kg? 
 SSC MTS 05/09/2023 (1st Shift) 
 (a) 225  (b) 218  (c) 222  (d) 220 
 Q.32.  Two  containers  of  equal  capacity 
 are  full  of  a  mixture  of  milk  and  water.  In 
 the  ?rst  container,  the  ratio  of  milk  to 
 water  is  3  :11  and  in  the  second 
 container  the  ratio  is  9  :11.  If  both  the 
 mixtures  are  mixed  in  a  container,  what  is 
 the resulting ratio of milk to water? 
 SSC MTS 06/09/2023 (2nd Shift) 
 (a) 87 : 197  (b) 21 : 87 
 (c) 93 : 187  (d) 93 : 179 
 Q.33.  There  are  two  varieties  of  rice. 
 Variety  1  costs  ?100  per  kg  and  variety  2 
 costs  ?120  per  kg.  The  vendor  mixed 
 both  the  varieties  and  sold  for  ?121  per 
 kg  and  gained  10%.  Find  the  ratio  of 
 variety 1 to variety 2 rice in the mixture. 
 SSC MTS 08/09/2023 (1st Shift) 
 (a) 1 : 1  (b) 3 : 1  (c) 2 : 1  (d) 1 : 3 
 Q.34.  Tea  leaves  worth  ?108  per  kg  and 
 ?120  per  kg  are  mixed  with  a  third  variety 
 in  the  ratio  2  :  3  :  5.  If  the  mixture  is  worth 
 ?125  per  kg,  the  price  (in  ?,  rounded  off 
 to  the  nearest  integer)  of  the  third  variety 
 of tea leaves per kg will be: 
 SSC MTS 08/09/2023 (3rd Shift) 
 (a) 130  (b) 128  (c) 135  (d) 133 
 Q.35.  In  some  quantity  of  water,four 
 times  the  quantity  of  milk  is  added  and 
 the  quantity  of  the  mixture  is  now  7.5 
 litres.  How  much  more  milk  is  to  be 
 added  to  the  mixture  to  have  90%  milk  in 
 the mixture ? 
 SSC MTS 11/09/2023 (1st Shift) 
 (a) 9 liters  (b) 9.5 liters 
 (c) 6 liters  (d) 7.5 liters 
 Q.36.  15  kg  of  ?25  per  kg  wheat  is  mixed 
 with  10  kg  of  another  type  of  wheat  to 
 get  a  mixture  costing  ?30  per  kg.  Find  the 
 price (per kg) of the costlier wheat. 
 SSC MTS 13/09/2023 (1st Shift) 
 (a) ?37.5  (b) ?32.5  (c) ?35.5  (d) ?30.5 
 Q.37.  A  mixture  contains  spirit  and  water 
 in  the  ratio  3  :  2.  If  2  litres  of  water  is 
 added  to  the  mixture,  the  ratio  becomes 
 5  :  4,  Find  the  quantity  of  spirit  in  the 
 mixture (in litres). 
 SSC MTS 13/09/2023 (2nd Shift) 
 (a) 15  (b) 20  (c) 25  (d) 10 
 Q.38.  In  what  ratio  should  rice  worth 
 ?140  per  kg  and  ?90  per  kg  be  mixed  so 
 that  a  mixture  of  two  qualities  of  rice 
 may become worth  ?110 per kg? 
 SSC MTS 14/09/2023 (3rd Shift) 
 (a) 2 : 3  (b) 1 : 3   (c) 3 : 2  (d) 1 : 2 
 SSC CHSL 2023 Tier - 1 
 Q.39.  A bottle is ?lled with liquid of which 
 4  parts  are  water  and  5  parts  are  fruit 
 extract.  How  much  of  the  mixture  must 
 be  drawn  off  and  replaced  with  water  so 
 that  the  mixture  may  be  half  water  and 
 half fruit extract ? 
 SSC CHSL 03/08/2023 (3rd Shift) 
 (a)  (b)  (c)  (d) 
 1 
 10 
 9 
 10 
 4 
 9 
 5 
 9 
 Q.40.  How  much  chicory,  costing 
 ?100/kg  should  be  added  to  40  kg  of 
 coffee  costing  ?45/kg  so  that  the  mixture 
 will be worth ?60/kg ? 
 SSC CHSL 03/08/2023 (3rd Shift) 
 (a) 12.5 kg (b) 5 kg (c) 17.5 kg (d) 15 kg 
 Q.41.  Milk  and  water  in  two  vessels  A 
 and  B  are  in  the  ratio  5  :  3  and  2  :  3, 
 respectively.  In  what  ratio  should  the 
 liquids  in  both  the  vessels  be  mixed  to 
 obtain  a  new  mixture  in  vessel  C 
 containing half milk and half water ? 
 SSC CHSL 04/08/2023 (1st Shift) 
 (a) 3 : 4  (b) 4 : 5  (c) 2 : 3   (d) 3 : 5 
 Q.42.  In  two  alloys,  the  ratio  of 
 Aluminium  to  Zinc  are  5  :  6  and  3  :  5.  If 
 242  kg  of  the  ?rst  alloy  and  144  kg  of  the 
 second  alloy  are  mixed,  then  the  ratio  of 
 Aluminium  and  Zinc  in  the  new  alloy  will 
 be: 
 SSC CHSL 07/08/2023 (4th Shift) 
 (a) 76 : 117  (b) 82 : 111 
 (c) 93 : 100  (d) 68 : 125 
 Q.43.  In  what  ratio  does  a  grocer  mix  tea 
 at  ?26  per  kg  and  ?32  per  kg  so  that  by 
 selling  the  mixture  at  ?30  per  kg  they 
 may gain 10%. ? 
 SSC CHSL 08/08/2023 (2nd Shift) 
 (a) 7 : 26  (b) 16 : 7   (c) 26 : 7   (d) 7 : 16 
 Q.44.  In  what  ratio,  wheat  at  ?23  per  kg 
 should  be  mixed  with  wheat  at  ?  14  per 
 kg  so  that  on  selling  the  mixture  at  ?  20 
 per kg there is a pro?t of 25% ? 
 SSC CHSL 09/08/2023 (1st Shift) 
 (a) 5 : 7    (b) 3 : 5     (c) 2 : 3    (d) 2 : 7 
 Q.45.  One  litre  milk  costs  ?40.  Water  is 
 mixed  with  milk  and  the  mixture  was  sold 
 at  ?30  per  litre.  Find  the  ratio  of  water 
 and milk in the mixture 
 SSC CHSL 09/08/2023 (3rd Shift) 
 (a)  2 : 5   (b)  1 : 3   (c)  1 : 2   (d)  2 : 3 
 Q.46.  In  a  mixture  of  178  litres,  the  ratio 
 of  water  and  milk  is  5  :  7.  How  much 
 water should be added to make the ratio 
 of water and milk 3 : 4 ? 
 SSC CHSL 10/08/2023 (1st Shift) 
 (a) 3  liters  (b)  liters 
 17 
 24 
 3 
 13 
 24 
 (c) 2  liters  (d) 2  liters 
 11 
 24 
 23 
 24 
 Q.47.  In  a  mixture,  the  ratio  of  a  chemical 
 X  and  water  is  15  :  9.  When  48  litres  of 
 this  mixture  is  replaced  with  water,  the 
 ratio  becomes  11  :  13.  Find  the  quantity 
 of water after replacement. 
 SSC CHSL 10/08/2023 (2nd Shift) 
 (a) 97.5 litres  (b) 99 litres 
 (c) 92 litres  (d) 102.5 litres 
 Q.48.  A  grocer  mixes  two  varieties  of  tea 
 priced  at  ?80  kg  and  ?85/kg  in  a  certain 
 ratio  to  produce  a  new  variety  priced  at 
 ?82/kg.  What  is  the  ratio  in  which  the  two 
 varieties  were  mixed  to  obtain  the  new 
 variety ? 
 SSC CHSL 10/08/2023 (3rd Shift) 
 (a) 1 : 3   (b) 2 : 5   (c) 4 : 4   (d) 3 : 2 
 Q.49.  Rice  worth  ?504  per  kg  and  ?540 
 per  kg  are  mixed  with  the  third  variety  in 
 the  ratio  1  :  1  :  2.  If  the  mixture  is  worth 
 ?612  per  kg,  ?nd  the  price  (per  kg  in  ?)  of 
 the third variety. 
 SSC CHSL 10/08/2023 (4th Shift) 
 (a) 630  (b) 702  (c) 764  (d) 522 
 Q.50.  How  many  kilograms  of  rice 
 costing  ?52  per  kg  must  be  mixed  with 
 35  kg  of  rice  costing  ?45  per  kg  so  as  to 
 get  a  gain  of  10%  by  selling  the  resulting 
 mixture of rice at the rate of ?55 per kg ? 
 SSC CHSL 11/08/2023 (2nd Shift) 
 (a) 87.5 kg  (b) 90.0 kg 
 (c) 85.0 kg  (d) 82.5 kg 
 Q.51.  In  an  experiment,  it  was  observed 
 that  metal  A  is  19  times  heavier  than 
 water  and  metal  B  is  9  times  heavier  than 
 water.  In  what  ratio  metal  A  and  B  mixed 
 so  that  the  mixture  thus  obtained  be  15 
 times heavier than water ? 
 SSC CHSL 11/08/2023 (3rd Shift) 
 (a) 2 : 3   (b) 1 : 3   (c) 3 : 1   (d) 3 : 2 
 Q.52.  Two  jars  A  and  B  are  containing 
 the  solutions  of  two  liquids  P  and  Q  .  The 
 ratio  of  the  liquids  P  and  Q  in  the  jars  A 
 and  B  are  2:  19  and  1:  11,  respectively.  If 
 7  litres  of  the  solution  of  jar  A  and  4  litres 
 of  the  solution  of  jar  B  are  mixed,  what  is 
 the  ratio  of  the  solutions  P  and  Q  in  the 
 new mixture ? 
 SSC CHSL 11/08/2023 (4th Shift) 
 (a) 10 : 1    (b) 1 : 9   (c) 9 : 1   (d) 1 : 10 
 Q.53.  If two qualities of a fruit costing 
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 Pinnacle  Day: 54th  Mixture and Alligation 
 ?20  per  kg  and  ?38  per  kg  are  mixed  in 
 the  ratio  of  5  :  4,  then  ?nd  the  cost  of  the 
 mixture per kg (in ?). 
 SSC CHSL 14/08/2023 (2nd Shift) 
 (a) 30  (b) 31  (c) 29  (d) 28 
 Q.54.  A  10-litre  solution  of  milk  and 
 water  contains  8  litres  of  milk.  2  litres  of 
 the  solution  is  replaced  by  pure  milk  and 
 mixed.  The  process  is  repeated  two  more 
 times.  How  much  milk  (in  litres)  is 
 present in the mixture so obtained ? 
 SSC CHSL 14/08/2023 (3rd Shift) 
 (a) 8.976  (b) 8.597  (c) 8.796  (d) 8.679 
 Q.55.  A  mixture  of  70  litres  of  wine  and 
 water  contains  10%  of  water.  How  much 
 water must be added to make the water 
 12  % of the resulting mixture ? 
 1 
 2 
 SSC CHSL 14/08/2023 (4th Shift) 
 (a) 5 litres  (b) 3 litres 
 (c) 2 litres  (d) 4 litres 
 Q.56.  A  cask  having  a  capacity  of  600 
 litres  is  initially  ?lled  with  wine.  From  this 
 cask  y  litres  of  wine  are  ?rst  drawn  and 
 replaced  with  water.  From  the  mixture, 
 120  litres  are  drawn  and  replaced  with 
 water.  From  this  further  diluted  mixture, 
 120  litres  are  drawn  again  and  replaced 
 with  water.  The  ratio  of  wine  to  water  in 
 the  cask  is  now  12  :  13.  What  is  the  value 
 of y ? 
 SSC CHSL 17/08/2023 (1st Shift) 
 (a) 125  (b) 150  (c) 200  (d) 100 
 Q.57.  A  mixture  contains  liquid  A  and  B 
 in  the  ratio  5  :  3,  respectively.  If  3  litres  of 
 liquid  B  is  added  to  it,  the  ratio  of  liquid  A 
 to  liquid  B  becomes  7  :  6.  What  is  the 
 quantity of liquid A in the mixture ? 
 SSC CHSL 17/08/2023 (3rd Shift) 
 (a) 7  litres  (b) 9  litres 
 2 
 3 
 1 
 3 
 (c) 11  litres  (d) 13  litres 
 2 
 3 
 1 
 3 
 SSC CGL 2023 Tier - 1 
 Q.58.  In what ratio must water be mixed 
 with milk, costing ?32 per litre, in order to 
 get a mixture costing ?28 per litre? 
 SSC CGL 14/07/2023 (2nd shift) 
 (a) 8 : 1    (b) 1 : 7   (c) 1 : 8  (d) 7 : 1 
 Q.59.  In  a  mixture  of  55  litres,  fruit  juice 
 and  water  are  in  the  ratio  of  4  :  1.  How 
 much water (in litres) must be added to 
 make the mixture ratio 2 : 1 ? 
 SSC CGL 14/07/2023 (4th shift) 
 (a) 9    (b) 22     (c) 11     (d) 12 
 Q.60.  One  quality  of  rice  at  ?45  per  kg  is 
 mixed  with  another  quality  at  a  certain 
 rate  in  the  ratio  of  3  :  2.  If  the  mixture  so 
 formed  is  worth  ?50  per  kg,  what  is  the 
 rate per kg of the second quality of rice? 
 SSC CGL 17/07/2023 (3rd shift) 
 (a) ?57   (b) ?57.5   (c) ?58   (d) ?58.5 
 Q.61.  If  two  qualities  of  pulses  'X'  and  'Y' 
 of  prices  ?100  and  ?150  per  kg  are  mixed 
 in  the  ratio  7  :  20,  then  what  is  the  price 
 (in  ?)  of  this  mixture  of  pulses  (correct  to 
 the nearest Rupee) ? 
 SSC CGL 18/07/2023 (2nd shift) 
 (a) 137   (b) 135   (c) 134   (d) 136 
 Q.62.  Rice  worth  ?126  per  kg  and  ?135 
 per  kg  are  mixed  with  a  third  variety  in 
 the  ratio  of  1  :  1  :  2.  If  the  mixture  is 
 worth  ?153  per  kg,  then  the  price  of  the 
 third variety per kg (in  ?) is: 
 SSC CGL 21/07/2023 (2nd shift) 
 (a) 182.5  (b) 195.5   (c) 133.5  (d) 175.5 
 Q.63.  A  40  -  litre  mixture  contains  25% 
 alcohol  and  75%  water.  If  10  litres  of  water 
 are  added  to  the  mixture,  the  percentage  of 
 alcohol in the new mixture is: 
 SSC CGL 25/07/2023 (4th shift) 
 (a) 27%     (b) 18%     (c) 20%    (d) 25% 
 SSC Selection Post (Phase - XI) 
 Q.64.  If  36  litres  of  20%  milk  solution  is 
 mixed  with  48  litres  of  10%  milk  solution, 
 then  what  will  be  the  percentage 
 concentration  of  milk  in  the  ?nal 
 solution? 
 Higher Secondary 27/06/2023 (Shift - 3) 
 (a) 14.28%  (b) 15.48% 
 (c) 12.38%  (d) 13.36% 
 Q.65.  A  merchant  bought  two  qualities  of 
 rice  at  the  rate  of  Rs.120/kg  and 
 Rs.220/kg.  In  72kg  of  the  second  quality 
 rice,  how  much  rice  (in  kg)  of  the  ?rst 
 quality  should  be  mixed  so  that  the 
 resulting  mixture  may  be  sold  at  the  rate 
 of Rs.280/kg to earn a pro?t of 40% 
 Matriculation Level 27/06/2023 (Shift - 2) 
 (a) 20  (b) 22  (c) 15  (d) 18 
 SSC MTS 2022 Tier - 1 
 Q.66.  In  A  mixture  of  180  litres,  the  ratio 
 of  milk  and  water  is  5  :  1.  If  this  ratio  is  to 
 be  3  :  2,  then  ?nd  the  quantity  of  water  to 
 be further added ? ( in litres ) 
 SSC MTS 03/05/2023 (Afternoon) 
 (a) 66  (b) 70      (c) 88  (d) 72 
 Q.67.  There  are  three  cups  of  mixture  of 
 milk  and  water  in  ratio  4  :  5,  5  :  6,  9  :  7. 
 36  liters  of  ?rst  and  44  liters  of  second 
 cup  are  taken.  How  much  quantity  from 
 third  cup  is  to  be  taken  so  that  ?nal 
 mixture  from  the  three  cups  will  have 
 milk and water in ratio 1 : 1 ? ( in litres ) 
 SSC MTS 10/05/2023 (Afternoon) 
 (a) 32  (b) 64     (c) 54        (d) 60 
 Q.68.  In a 64 litres mixture , the alcohol 
 and  water  are  in  the  ratio  of  1  :  3 
 respectively.  32  litres  of  mixture  is  taken 
 off  and  replaced  with  16  litres  of  water. 
 What  is  the  new  ratio  of  alcohol  and 
 water respectively ? 
 SSC MTS 19/05/2023 (Evening) 
 (a) 1 : 5      (b) 5 : 12    (c) 2 : 7    (d) 3 : 10 
 Q.69.  135  kg  of  an  alloy  A  is  mixed  with 
 72  kg  of  alloy  B  to  get  a  new  alloy.  If  alloy 
 A  has  zinc  and  copper  in  the  ratio  4  :  5 
 and  alloy  B  has  zinc  and  copper  in  ratio  7 
 :  5,  then  what  is  the  weight  of  zinc  in  the 
 new alloy? 
 SSC MTS 13/06/2023 (Morning) 
 (a) 102 kg  (b) 115 kg  (c) 85 kg (d) 92 kg 
 Q.70.  One  liquid  contains  20%  of  acid  and 
 the  other  liquid  contain  30%  of  acid.  A  can 
 is  ?lled  with  7  parts  of  the  ?rst  liquid  and 
 3  parts  of  the  second  liquid.  The 
 percentage  of  the  acid  in  the  new  mixture 
 is : 
 SSC MTS 15/06/2023 (Morning) 
 (a) 13%  (b) 30%  (c) 14%  (d) 23% 
 Q.71.  Mixture  of  milk  and  water  in  three 
 bottles  of  equal  capacity  is  in  the  ratio  4  : 
 1,  4  :  3  and  1  :  2  respectively.  These  three 
 bottles  are  emptied  into  a  large  bottle. 
 What  will  be  the  ratio  of  milk  and  water 
 respectively in the large bottle? 
 SSC MTS 15/06/2023 (Morning) 
 (a) 179 : 136  (b) 152 : 165 
 (c) 198 : 175  (d) 133 : 145 
 Q.72.  The  alcohol  and  water  in  a  mixture 
 are  in  the  ratio  of  4  :  5  respectively.  20 
 litre  water  is  added  to  it.  If  the  ratio  of 
 alcohol  and  water  in  the  new  mixture  is  1 
 :  3  respectively,  then  what  is  the  total 
 quantity  of  the  alcohol  in  the  new 
 mixture? 
 SSC MTS 16/06/2023 (Morning) 
 (a)  litres  (b) 15 litres 
 80 
 7 
 (c)  litres  (d)  litres 
 60 
 7 
 90 
 11 
 Q.73.  The  ratio  of  spirit  and  water  in  two 
 mixtures  of  46  litres  and  50  litres  is  11  : 
 12  and  2  :  3  respectively.  Both  the 
 mixtures  are  mixed.  Find  the  ratio  of  the 
 spirit and water in the new mixture. 
 SSC MTS 16/06/2023 (Evening) 
 (a) 8 : 9  (b) 7 : 9  (c) 5 : 6  (d) 3 : 7 
 Q.74.  An  alloy  contains  copper,  zinc  and 
 nickel  in  the  ratio  of  3  :  2  :  5  respectively. 
 What  quantity  of  nickel  (in  kg)  must  be 
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Page 5


 Pinnacle  Day: 54th  Mixture and Alligation 
 Mixture and Alligation 
 Mixture  :  when  two  or  more  than  two 
 substances  mixed  together  in  any  ratio  to 
 produce a product is called mixture . 
 Mean  price  :  the  average  of  all  the  given 
 prices  of  the  known  items  is  called  Mean 
 Price . 
 1.  Alligation  rule  :  It  is  used  to  ?nd  the 
 ratio  in  which  two  or  more  substances  at 
 their  respective  prices  should  be  mixed 
 to produce a mixture at a given price. 
 where 
 C = Cost price of cheaper 
 D = Cost price of dearer 
 M = Mean price 
 (D - M) = Cheaper quantity 
 (M - C) = Dearer quantity 
 2. Quantity of pure liquid  =  ?? (
 ??    -    ?? 
 ?? 
)
 ?? 
 where,  =  Quantity  of  original  liquid,  =  ??  ?? 
 Quantity  to  be  carried  out  and  replaced,  ?? 
 =  Number  of  times  the  operation  is 
 conducted 
 Important Cases :- 
 Case 1  : 
 Ratio  of  milk  and  water  in  container  A,  B 
 and  C  are  1  :  2,  4  :  1  and  4  :  5 
 respectively.  Find  the  ratio  in  which 
 containers  A  and  B  are  mixed  to  get  4  :  5 
 in container C ? 
 Soln :  Fraction of milk in container A = 
 1 
 3 
 Fraction of milk in container B = 
 4 
 5 
 Fraction of milk in container C = 
 4 
 9 
 So, the required ratio = 16 : 5 
 Case 2  : 
 Ratio  of  milk  and  water  in  container  A 
 and  B  are  3  :  1  and  4  :  1  respectively. 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  Find  the  ratio  of 
 quantity of milk and water in container C. 
 Soln : 
 Fraction of milk in container A = 
 3 
 4 
 Fraction of milk in container B = 
 4 
 5 
 Ratio  in  which  container  A  and  B  are  to 
 be  mixed  is  2  :  1.  So,  let  the  quantity  in 
 container  A  and  B  be  2  litre  and  1  litre 
 respectively. 
 So, the required ratio = 
 [  2  ]  +  [  1] : [  2]  +  [  1] 
 3 
 4 
×
 4 
 5 
×
 1 
 4 
×
 1 
 5 
×
 =  +  :  +  =  :  = 23 : 7 
 3 
 2 
 4 
 5 
 1 
 2 
 1 
 5 
 23 
 10 
 7 
 10 
 Case  3  :  Two  varieties  costing  ?4/kg  and 
 ?5/kg  respectively  are  mixed  in  3  :  2.  Find 
 the  cost  price  per  kg  of  the  resultant 
 mixture? 
 Soln: 
 A 
 wt 
 =  = 
 ??  1  ??  1    +    ??  2  ??  2 
 ??  1    +    ??  2 
 4     ×     3    +    5     ×     2 
 3    +    2 
 =  =  = 4.4 kg 
 12    +    10 
 5 
 22 
 5 
 Variety Questions 
 Q.1.  80  litres  of  a  mixture  of  spirit  and 
 water  in  the  ratio  7  :  9  is  present  in  a 
 container  A.  20  litres  of  the  mixture  is 
 transferred  to  another  container  B.  Then 
 the  container  A  is  ?lled  with  20  litres  of 
 water.  Then  32  litres  of  the  mixture  is 
 again  transferred  to  container  B.  The 
 ratio  of  water  to  spirit  of  the  mixture  in 
 container B is equal to: 
 SSC CGL Tier II  (26/10/2023) 
 (a) 41 : 87  (b) 87 : 41 
 (c) 131 : 77  (d) 77 : 131 
 Q.2.  At  a  certain  time  in  a  park,  the 
 number  of  heads  and  the  number  of  legs 
 of  monkeys  and  human  visitors  were 
 counted,  and  it  was  found  that  there  were 
 54  heads  and  148  legs.  Find  the  number 
 of monkeys in the park. 
 SSC CGL Tier II  (26/10/2023) 
 (a) 20  (b) 16  (c) 18  (d) 14 
 Q.3.  A  milk  vendor  has  2  vessels  of  milk 
 and  water.  The  ?rst  contains  80%  milk 
 and  the  rest  is  water.  The  second 
 contains  50%  milk.  How  much  mixture  (in 
 L)  should  he  mix  from  each  of  the 
 vessels  so  as  to  get  9  litres  of  mixture 
 such  that  the  ratio  of  water  to  milk  is  1  :  2 
 ?  (Write  your  answer  in  the  order  of 
 vessel 1 and vessel 2) 
 SSC MTS 13/09/2023 (1st Shift) 
 (a) 6, 3  (b) 4, 5  (c) 3, 6  (d) 5, 4 
 Q.4.  A  blended  tea  in  a  barrel  contains 
 Assam,  Darjeeling  and  Nilgiri  Hills  in  the 
 ratio  2  :  3  :  1.  Another  barrel  contains 
 Darjeeling,  Nilgiri  Hills  and  Kangra  Valley 
 in  the  ratio  5  :  4  :  3.  If  equal  weights  of 
 both  blended  tea  mix  together  to  make  a 
 new brand, then the weight of Kangra 
 Valley per kilogram in the new brand is: 
 SSC CHSL 10/08/2023 (3rd Shift) 
 (a) 500 gm  (b) 100 gm 
 (c) 250 gm  (d) 125 gm 
 Q.5.  From  a  cask  of  milk  containing  64 
 liters,  8  liters  are  drawn  out  and  the  cask 
 is  ?lled  up  with  water.  If  the  same 
 process  is  repeated  a  second,  then  a 
 third  time,  what  will  be  the  proportion  of 
 milk to water in the resulting mixture ? 
 SSC CHSL 09/08/2023 (2nd Shift) 
 (a) 343 : 179  (b) 333 : 169 
 (c) 443 : 179  (d) 343 : 169 
 Q.6.  A  jar  contains  35%  syrup  in  the 
 mixture  of  syrup  and  water.  A  part  of  this 
 mixture  is  replaced  by  another  mixture 
 containing  20%  syrup.  Now,  in  the  new 
 mixture,  the  percentage  of  syrup  is  found 
 to  be  24%.  What  is  the  ratio  in  which 
 these  mixtures  were  mixed  to  obtain  the 
 new mixture ? 
 SSC CHSL 07/08/2023 (2nd Shift) 
 (a) 3 : 14  (b) 4 : 11  (c) 5 : 13  (d) 7 : 10 
 Q.7.  In  a  solution  of  water  and  milk,  the 
 quantity  of  milk  is  double  the  quantity  of 
 water.  To  pass  the  quality  standards,  the 
 solution  must  contain  90%  milk  in  it.  If 
 the  volume  of  the  solution  is  v,  then  how 
 much  pure  milk  in  litres  is  to  be  added  to 
 the solution to pass the quality standard. 
 SSC CHSL 02/08/2023 (2nd Shift) 
 (a)  v  (b)  v  (c)  v  (d)  v 
 4 
 3 
 3 
 4 
 7 
 4 
 7 
 3 
 Q.8.  A  vessel  is  ?lled  with  liquid,  5  parts 
 of  which  are  water  and  11  parts  syrup. 
 What  part  of  the  mixture  must  be  drawn 
 off  and  replaced  with  water  so  that  the 
 mixture  may  be  syrup  and  water  in  the 
 ratio 3 : 2 ? 
 SSC CGL 26/07/2023 (1st shift) 
 (a)  (b)  (c)  (d) 
 14 
 45 
 27 
 35 
 36 
 65 
 7 
 55 
 Q.9.  Alloy  X  contains  70%  copper  and 
 30%  zinc.  Alloy  Y  contains  40%  copper, 
 25%  zinc  and  35%  aluminum.  Alloy  X  and 
 Y  are  mixed  in  the  ratio  of  1  :  3.  What  is 
 the  ratio  of  copper  and  zinc  in  the  newly 
 formed alloy ? 
 SSC MTS 17/05/2023 (Afternoon) 
 (a) 19 : 33  (b) 11 : 32 
 (c) 38 : 21  (d) 19 : 21 
 Q.10.  A  jar  contains  a  mixture  of  milk 
 and  water,  having  50%  water.  A  part  of 
 this  mixture  is  replaced  by  another 
 mixture  having  29%  water.  The 
 percentage  of  water  in  the  jar  after 
 replacement  is  36%.  What  fraction  of  the 
 original mixture was replaced ? 
 SSC MTS 10/05/2023 (Afternoon) 
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 (a)  (b)  (c)  (d) 
 3 
 2 
 4 
 5 
 1 
 3 
 2 
 3 
 Q.11.  A  100  ml  solution  of  having  ?? 
 2 
 ???? 
 4 
 concentration  of  20%  is  mixed  with  a 
 50%  concentrated  x  ml  mixture  such  that 
 the  net  mixture  is  30%  concentrated. 
 Determine x. 
 SSC CGL  08/12/2022 (1st Shift) 
 (a) 70 ml  (b) 80 ml  (c) 60 ml  (d) 50 ml 
 Q.12.  The  cost  of  two  varieties  of  tea  is 
 ?300  and  ?375  respectively.  If  both  the 
 varieties  of  tea  are  mixed  together  in  the 
 ratio  3  :  2,  then  what  should  be  the  price 
 of the mixed variety of tea per kg? 
 SSC CPO 09/11/2022 (Morning) 
 (a) ?340 (b) ?330 (c) ?350 (d) ?360 
 Q.13.  Two  vessels  of  equal  capacity,  and 
 both  completely  ?lled,  contain  mixtures 
 of  milk  and  water  in  the  ratio  5  :  1  and  6  : 
 5,  respectively.  Both  the  mixtures  are 
 now  mixed  thoroughly.  What  is  the  ratio 
 of  milk  to  water  in  the  new  mixture  so 
 obtained? 
 SSC MTS 13/07/2022 (Evening) 
 (a) 105 : 67  (b) 57 : 41 
 (c) 91 : 41  (d) 28 : 43 
 Q.14.  Babulal  runs  a  juice  corner  outside 
 a  park  and  sells  giloy  juice  (giloy  +  water) 
 in  the  morning.  Initially  he  had  19  litres  of 
 juice,  which  had  giloy  and  water  in  the 
 ratio  2  :  9.  He  sold  2  litres  of  juice. 
 1 
 2 
 Later,  in  order  to  dilute  it,  he  added  some 
 water  and  the  ratio  of  giloy  and  water 
 became  1  :  5.  How  much  water  was 
 added ? 
 SSC MTS 27/10/2021 (Morning) 
 (a) 1  litres  (b)  litre 
 1 
 2 
 1 
 2 
 (c)  2 litres  (d) 1 litre 
 Q.15.  Alloy  A  contains  metal  x  and  y  only 
 in  the  ratio  5  :  2  and  alloy  B  contains 
 these  metals  in  the  ratio  3  :  4.  Alloy  C  is 
 prepared by mixing A and B in the ratio 
 4 : 5. The percentage of x in alloy C is: 
 SSC CGL Tier II (16/11/2020) 
 (a) 44  (b) 56  (c) 45  (d) 55 
 4 
 9 
 5 
 9 
 Q.16.  Two  bottles  of  same  capacity  are 
 35%  and  33  %  full  of  orange  juice, 
 1 
 3 
 respectively.  They  are  ?lled  up 
 completely  with  apple  juice  and  then  the 
 contents  of  both  bottles  are  emptied  into 
 another  vessel.  The  percentage  of  apple 
 juice in the mixture is: 
 SSC CGL 03/03/2020 (Afternoon) 
 (a) 34  (b) 64  (c) 60  (d) 65 
 1 
 6 
 1 
 3 
 2 
 3 
 5 
 6 
 Q.17.  A  vessel  contains  a  32  litre 
 solution  of  acid  and  water  in  which  the 
 ratio  of  acid  and  water  is  5  :  3.  If  12  litres 
 of  the  solution  are  taken  out  and  7 
 1 
 2 
 litres  of  water  are  added  to  it,  then  what 
 is  the  ratio  of  acid  and  water  in  the 
 resulting solution ? 
 SSC CGL Tier II (13/09/2019) 
 (a) 4 : 7  (b) 5 : 6  (c) 4 : 9  (d) 8 : 11 
 Q.18.  The  ratios  of  copper  to  Zinc  in  alloys 
 A  and  B  are  3  :  4  and  5  :  9  respectively.  A 
 and  B  are  taken  in  the  ratio  2:3  and  melted 
 to  form  a  new  alloy  C.  What  is  the  ratio  of 
 copper to Zinc in C ? 
 SSC CGL Tier II (11/09/2019) 
 (a) 8 : 13  (b) 3 : 5  (c) 9 : 11  (d) 27 : 43 
 Q.19.  A  mixture  contains  milk  and  water 
 in  the  ratio  (by  volume)  5  :  3  and  another 
 mixture,  of  the  same  volume  as  that  of 
 the  former,  contains  water  and  milk  in  the 
 ratio  (by  volume)  1  :  3.  In  what  ratio,  two 
 mixture  be  mixed  in  order  to  obtain  a  new 
 mixture  consisting  of  milk  and  water  in 
 the ratio (by volume) 7 : 3 ? 
 SSC MTS 13/08/2019 (Afternoon) 
 (a) 2 : 3  (b) 3 : 4  (c) 5 : 6  (d) 3 : 2 
 Q.20.  In  the  60  litre  mixture  of  milk  and 
 water,  the  quantities  of  milk  and  water 
 are  in  the  ratio  of  3  :  2.  If  we  want  to 
 make  the  ratio  of  the  quantities  of  milk 
 and  water  1  :  1,  then  how  much  extra 
 water should be put in the mixture ? 
 SSC MTS 05/08/2019 (Afternoon) 
 (a)10 litre (b) 16litre  (c)12 litre (d)14 litre 
 Q.21.  A  milkman  uses  three  containers 
 for  selling  milk,  their  capacities  being 
 40L,  30L  and  20L  respectively.  He  ?lls 
 respectively  87.5%,  80%  and  90%  of  the 
 containers  with  a  mix  of  milk  and  water 
 in  the  ratios,  3  :  2,  5  :  1  and  7  :  2 
 respectively.  What  is  the  ratio  of  total 
 quantity  of  milk  to  that  of  water  carried 
 by him ? 
 SSC CHSL 10/07/2019 (Evening) 
 (a) 7 : 2  (b) 31 : 12   (c) 35 : 9   (d) 5 : 2 
 Q.22.  Fresh  fruit  contains  68%  water  and 
 dry  fruit  contains  20%  water.  How  much 
 dry  fruit  can  be  obtained  from  100  kg  of 
 fresh fruit 
 SSC CPO 16/03/2019 (Morning) 
 (a) 80  (b) 60  (c) 40  (d) 20 
 Practice Questions 
 SSC CPO 2023 Tier - 1 
 Q.23.  If 60 liters of a milk solution has 
 40% milk in it, then how much milk 
 should  be  added  to  make  the  milk  60%  in 
 the solution? 
 SSC CPO 03/10/2023 (3rd Shift) 
 (a) 30 liters  (b) 20 liters 
 (c) 35 liters  (d) 25 liters 
 Q.24.  Two  mixtures  A  and  B  have  the 
 following compositions: 
 Mixture  A  has  copper  and  tin  in  a  ratio  of 
 1 : 2 
 Mixture  B  has  copper  and  tin  in  a  ratio  of 
 1 : 3 
 If  equal  quantities  of  mixtures  A  and  B 
 are  used  for  producing  mixture  C,  then 
 ?nd  the  ratio  of  copper  and  tin  in  mixture 
 C. 
 SSC CPO 04/10/2023 (3rd Shift) 
 (a) 2 : 5    (b) 7 : 17    (c) 7 : 12    (d) 1 : 5 
 SSC MTS 2023 Tier -1 
 Q.25.  There  is  a  25  litre  mixture  of  milk 
 and  water,  containing  milk  and  water  in 
 the  ratio  3  :  2.  Find  the  number  of  litres  of 
 water  that  should  be  added  to  the 
 mixture  so  that  the  resultant  mixture  has 
 50% water in it. 
 SSC MTS 01/09/2023 (2nd Shift) 
 (a) 10  (b) 8  (c) 5  (d) 12 
 Q.26.  From  a  container  having  pure  milk, 
 35%  is  replaced  by  water  and  the  process 
 is  repeated  thrice.  At  the  end  of  the  third 
 operation, the purity of the milk is: 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 21  %  (b) 37  % 
 23 
 80 
 21 
 80 
 (c) 23  %  (d) 27  % 
 37 
 80 
 37 
 80 
 Q.27.  In  what  ratio  must  a  grocer  mix  two 
 varieties  of  pulses  costing  ?18  per  kg 
 and  ?22  per  kg,  respectively,  so  as  to  get 
 a mixture worth ?19.50 per kg? 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 5 : 3  (b) 5 : 1  (c) 1 : 5  (d) 5 : 2 
 Q.28.  How  many  kilograms  of  sugar  at 
 ?3.80  per  kg  must  be  mixed  with  60  kg  of 
 sugar  at  ?4.60  per  kg,  so  that  by  selling 
 the  mixture  at  ?5.20  per  kg  there  may  be 
 a gain of 30%? 
 SSC MTS 01/09/2023 (3rd Shift) 
 (a) 170 kg  (b) 120 kg  (c) 160 kg (d) 180 kg 
 Q.29.  A  mixture  contains  milk  and  water 
 in  the  ratio  9  :  7.  If  it  contains  4  litres 
 more  milk  than  water,  then  ?nd  the 
 quantity of milk (in litres) in the mixture. 
 SSC MTS 04/09/2023 (1st Shift) 
 (a) 18  (b) 15  (c) 21  (d) 14 
 Q.30.  A  vessel  contains  liquid  A  and 
 liquid  B  in  the  ratio  4  :  9.  If  8  litres  of 
 liquid  A  is  added  to  the  vessel,  the  new 
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 Pinnacle  Day: 54th  Mixture and Alligation 
 ratio  becomes  8  :  9.  Find  the  quantity  of 
 liquid A (in litres) in the original mixture. 
 SSC MTS 04/09/2023 (2nd Shift) 
 (a) 12  (b) 9  (c) 8  (d) 6 
 Q.31.  If  two  varieties  of  a  grain  worth 
 ?202  per  kg  and  ?250  per  kg, 
 respectively,  are  mixed  in  the  ratio  of  7  : 
 5,  then  what  is  the  cost  (in  ?)  of  the 
 resulting mixture per kg? 
 SSC MTS 05/09/2023 (1st Shift) 
 (a) 225  (b) 218  (c) 222  (d) 220 
 Q.32.  Two  containers  of  equal  capacity 
 are  full  of  a  mixture  of  milk  and  water.  In 
 the  ?rst  container,  the  ratio  of  milk  to 
 water  is  3  :11  and  in  the  second 
 container  the  ratio  is  9  :11.  If  both  the 
 mixtures  are  mixed  in  a  container,  what  is 
 the resulting ratio of milk to water? 
 SSC MTS 06/09/2023 (2nd Shift) 
 (a) 87 : 197  (b) 21 : 87 
 (c) 93 : 187  (d) 93 : 179 
 Q.33.  There  are  two  varieties  of  rice. 
 Variety  1  costs  ?100  per  kg  and  variety  2 
 costs  ?120  per  kg.  The  vendor  mixed 
 both  the  varieties  and  sold  for  ?121  per 
 kg  and  gained  10%.  Find  the  ratio  of 
 variety 1 to variety 2 rice in the mixture. 
 SSC MTS 08/09/2023 (1st Shift) 
 (a) 1 : 1  (b) 3 : 1  (c) 2 : 1  (d) 1 : 3 
 Q.34.  Tea  leaves  worth  ?108  per  kg  and 
 ?120  per  kg  are  mixed  with  a  third  variety 
 in  the  ratio  2  :  3  :  5.  If  the  mixture  is  worth 
 ?125  per  kg,  the  price  (in  ?,  rounded  off 
 to  the  nearest  integer)  of  the  third  variety 
 of tea leaves per kg will be: 
 SSC MTS 08/09/2023 (3rd Shift) 
 (a) 130  (b) 128  (c) 135  (d) 133 
 Q.35.  In  some  quantity  of  water,four 
 times  the  quantity  of  milk  is  added  and 
 the  quantity  of  the  mixture  is  now  7.5 
 litres.  How  much  more  milk  is  to  be 
 added  to  the  mixture  to  have  90%  milk  in 
 the mixture ? 
 SSC MTS 11/09/2023 (1st Shift) 
 (a) 9 liters  (b) 9.5 liters 
 (c) 6 liters  (d) 7.5 liters 
 Q.36.  15  kg  of  ?25  per  kg  wheat  is  mixed 
 with  10  kg  of  another  type  of  wheat  to 
 get  a  mixture  costing  ?30  per  kg.  Find  the 
 price (per kg) of the costlier wheat. 
 SSC MTS 13/09/2023 (1st Shift) 
 (a) ?37.5  (b) ?32.5  (c) ?35.5  (d) ?30.5 
 Q.37.  A  mixture  contains  spirit  and  water 
 in  the  ratio  3  :  2.  If  2  litres  of  water  is 
 added  to  the  mixture,  the  ratio  becomes 
 5  :  4,  Find  the  quantity  of  spirit  in  the 
 mixture (in litres). 
 SSC MTS 13/09/2023 (2nd Shift) 
 (a) 15  (b) 20  (c) 25  (d) 10 
 Q.38.  In  what  ratio  should  rice  worth 
 ?140  per  kg  and  ?90  per  kg  be  mixed  so 
 that  a  mixture  of  two  qualities  of  rice 
 may become worth  ?110 per kg? 
 SSC MTS 14/09/2023 (3rd Shift) 
 (a) 2 : 3  (b) 1 : 3   (c) 3 : 2  (d) 1 : 2 
 SSC CHSL 2023 Tier - 1 
 Q.39.  A bottle is ?lled with liquid of which 
 4  parts  are  water  and  5  parts  are  fruit 
 extract.  How  much  of  the  mixture  must 
 be  drawn  off  and  replaced  with  water  so 
 that  the  mixture  may  be  half  water  and 
 half fruit extract ? 
 SSC CHSL 03/08/2023 (3rd Shift) 
 (a)  (b)  (c)  (d) 
 1 
 10 
 9 
 10 
 4 
 9 
 5 
 9 
 Q.40.  How  much  chicory,  costing 
 ?100/kg  should  be  added  to  40  kg  of 
 coffee  costing  ?45/kg  so  that  the  mixture 
 will be worth ?60/kg ? 
 SSC CHSL 03/08/2023 (3rd Shift) 
 (a) 12.5 kg (b) 5 kg (c) 17.5 kg (d) 15 kg 
 Q.41.  Milk  and  water  in  two  vessels  A 
 and  B  are  in  the  ratio  5  :  3  and  2  :  3, 
 respectively.  In  what  ratio  should  the 
 liquids  in  both  the  vessels  be  mixed  to 
 obtain  a  new  mixture  in  vessel  C 
 containing half milk and half water ? 
 SSC CHSL 04/08/2023 (1st Shift) 
 (a) 3 : 4  (b) 4 : 5  (c) 2 : 3   (d) 3 : 5 
 Q.42.  In  two  alloys,  the  ratio  of 
 Aluminium  to  Zinc  are  5  :  6  and  3  :  5.  If 
 242  kg  of  the  ?rst  alloy  and  144  kg  of  the 
 second  alloy  are  mixed,  then  the  ratio  of 
 Aluminium  and  Zinc  in  the  new  alloy  will 
 be: 
 SSC CHSL 07/08/2023 (4th Shift) 
 (a) 76 : 117  (b) 82 : 111 
 (c) 93 : 100  (d) 68 : 125 
 Q.43.  In  what  ratio  does  a  grocer  mix  tea 
 at  ?26  per  kg  and  ?32  per  kg  so  that  by 
 selling  the  mixture  at  ?30  per  kg  they 
 may gain 10%. ? 
 SSC CHSL 08/08/2023 (2nd Shift) 
 (a) 7 : 26  (b) 16 : 7   (c) 26 : 7   (d) 7 : 16 
 Q.44.  In  what  ratio,  wheat  at  ?23  per  kg 
 should  be  mixed  with  wheat  at  ?  14  per 
 kg  so  that  on  selling  the  mixture  at  ?  20 
 per kg there is a pro?t of 25% ? 
 SSC CHSL 09/08/2023 (1st Shift) 
 (a) 5 : 7    (b) 3 : 5     (c) 2 : 3    (d) 2 : 7 
 Q.45.  One  litre  milk  costs  ?40.  Water  is 
 mixed  with  milk  and  the  mixture  was  sold 
 at  ?30  per  litre.  Find  the  ratio  of  water 
 and milk in the mixture 
 SSC CHSL 09/08/2023 (3rd Shift) 
 (a)  2 : 5   (b)  1 : 3   (c)  1 : 2   (d)  2 : 3 
 Q.46.  In  a  mixture  of  178  litres,  the  ratio 
 of  water  and  milk  is  5  :  7.  How  much 
 water should be added to make the ratio 
 of water and milk 3 : 4 ? 
 SSC CHSL 10/08/2023 (1st Shift) 
 (a) 3  liters  (b)  liters 
 17 
 24 
 3 
 13 
 24 
 (c) 2  liters  (d) 2  liters 
 11 
 24 
 23 
 24 
 Q.47.  In  a  mixture,  the  ratio  of  a  chemical 
 X  and  water  is  15  :  9.  When  48  litres  of 
 this  mixture  is  replaced  with  water,  the 
 ratio  becomes  11  :  13.  Find  the  quantity 
 of water after replacement. 
 SSC CHSL 10/08/2023 (2nd Shift) 
 (a) 97.5 litres  (b) 99 litres 
 (c) 92 litres  (d) 102.5 litres 
 Q.48.  A  grocer  mixes  two  varieties  of  tea 
 priced  at  ?80  kg  and  ?85/kg  in  a  certain 
 ratio  to  produce  a  new  variety  priced  at 
 ?82/kg.  What  is  the  ratio  in  which  the  two 
 varieties  were  mixed  to  obtain  the  new 
 variety ? 
 SSC CHSL 10/08/2023 (3rd Shift) 
 (a) 1 : 3   (b) 2 : 5   (c) 4 : 4   (d) 3 : 2 
 Q.49.  Rice  worth  ?504  per  kg  and  ?540 
 per  kg  are  mixed  with  the  third  variety  in 
 the  ratio  1  :  1  :  2.  If  the  mixture  is  worth 
 ?612  per  kg,  ?nd  the  price  (per  kg  in  ?)  of 
 the third variety. 
 SSC CHSL 10/08/2023 (4th Shift) 
 (a) 630  (b) 702  (c) 764  (d) 522 
 Q.50.  How  many  kilograms  of  rice 
 costing  ?52  per  kg  must  be  mixed  with 
 35  kg  of  rice  costing  ?45  per  kg  so  as  to 
 get  a  gain  of  10%  by  selling  the  resulting 
 mixture of rice at the rate of ?55 per kg ? 
 SSC CHSL 11/08/2023 (2nd Shift) 
 (a) 87.5 kg  (b) 90.0 kg 
 (c) 85.0 kg  (d) 82.5 kg 
 Q.51.  In  an  experiment,  it  was  observed 
 that  metal  A  is  19  times  heavier  than 
 water  and  metal  B  is  9  times  heavier  than 
 water.  In  what  ratio  metal  A  and  B  mixed 
 so  that  the  mixture  thus  obtained  be  15 
 times heavier than water ? 
 SSC CHSL 11/08/2023 (3rd Shift) 
 (a) 2 : 3   (b) 1 : 3   (c) 3 : 1   (d) 3 : 2 
 Q.52.  Two  jars  A  and  B  are  containing 
 the  solutions  of  two  liquids  P  and  Q  .  The 
 ratio  of  the  liquids  P  and  Q  in  the  jars  A 
 and  B  are  2:  19  and  1:  11,  respectively.  If 
 7  litres  of  the  solution  of  jar  A  and  4  litres 
 of  the  solution  of  jar  B  are  mixed,  what  is 
 the  ratio  of  the  solutions  P  and  Q  in  the 
 new mixture ? 
 SSC CHSL 11/08/2023 (4th Shift) 
 (a) 10 : 1    (b) 1 : 9   (c) 9 : 1   (d) 1 : 10 
 Q.53.  If two qualities of a fruit costing 
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 Pinnacle  Day: 54th  Mixture and Alligation 
 ?20  per  kg  and  ?38  per  kg  are  mixed  in 
 the  ratio  of  5  :  4,  then  ?nd  the  cost  of  the 
 mixture per kg (in ?). 
 SSC CHSL 14/08/2023 (2nd Shift) 
 (a) 30  (b) 31  (c) 29  (d) 28 
 Q.54.  A  10-litre  solution  of  milk  and 
 water  contains  8  litres  of  milk.  2  litres  of 
 the  solution  is  replaced  by  pure  milk  and 
 mixed.  The  process  is  repeated  two  more 
 times.  How  much  milk  (in  litres)  is 
 present in the mixture so obtained ? 
 SSC CHSL 14/08/2023 (3rd Shift) 
 (a) 8.976  (b) 8.597  (c) 8.796  (d) 8.679 
 Q.55.  A  mixture  of  70  litres  of  wine  and 
 water  contains  10%  of  water.  How  much 
 water must be added to make the water 
 12  % of the resulting mixture ? 
 1 
 2 
 SSC CHSL 14/08/2023 (4th Shift) 
 (a) 5 litres  (b) 3 litres 
 (c) 2 litres  (d) 4 litres 
 Q.56.  A  cask  having  a  capacity  of  600 
 litres  is  initially  ?lled  with  wine.  From  this 
 cask  y  litres  of  wine  are  ?rst  drawn  and 
 replaced  with  water.  From  the  mixture, 
 120  litres  are  drawn  and  replaced  with 
 water.  From  this  further  diluted  mixture, 
 120  litres  are  drawn  again  and  replaced 
 with  water.  The  ratio  of  wine  to  water  in 
 the  cask  is  now  12  :  13.  What  is  the  value 
 of y ? 
 SSC CHSL 17/08/2023 (1st Shift) 
 (a) 125  (b) 150  (c) 200  (d) 100 
 Q.57.  A  mixture  contains  liquid  A  and  B 
 in  the  ratio  5  :  3,  respectively.  If  3  litres  of 
 liquid  B  is  added  to  it,  the  ratio  of  liquid  A 
 to  liquid  B  becomes  7  :  6.  What  is  the 
 quantity of liquid A in the mixture ? 
 SSC CHSL 17/08/2023 (3rd Shift) 
 (a) 7  litres  (b) 9  litres 
 2 
 3 
 1 
 3 
 (c) 11  litres  (d) 13  litres 
 2 
 3 
 1 
 3 
 SSC CGL 2023 Tier - 1 
 Q.58.  In what ratio must water be mixed 
 with milk, costing ?32 per litre, in order to 
 get a mixture costing ?28 per litre? 
 SSC CGL 14/07/2023 (2nd shift) 
 (a) 8 : 1    (b) 1 : 7   (c) 1 : 8  (d) 7 : 1 
 Q.59.  In  a  mixture  of  55  litres,  fruit  juice 
 and  water  are  in  the  ratio  of  4  :  1.  How 
 much water (in litres) must be added to 
 make the mixture ratio 2 : 1 ? 
 SSC CGL 14/07/2023 (4th shift) 
 (a) 9    (b) 22     (c) 11     (d) 12 
 Q.60.  One  quality  of  rice  at  ?45  per  kg  is 
 mixed  with  another  quality  at  a  certain 
 rate  in  the  ratio  of  3  :  2.  If  the  mixture  so 
 formed  is  worth  ?50  per  kg,  what  is  the 
 rate per kg of the second quality of rice? 
 SSC CGL 17/07/2023 (3rd shift) 
 (a) ?57   (b) ?57.5   (c) ?58   (d) ?58.5 
 Q.61.  If  two  qualities  of  pulses  'X'  and  'Y' 
 of  prices  ?100  and  ?150  per  kg  are  mixed 
 in  the  ratio  7  :  20,  then  what  is  the  price 
 (in  ?)  of  this  mixture  of  pulses  (correct  to 
 the nearest Rupee) ? 
 SSC CGL 18/07/2023 (2nd shift) 
 (a) 137   (b) 135   (c) 134   (d) 136 
 Q.62.  Rice  worth  ?126  per  kg  and  ?135 
 per  kg  are  mixed  with  a  third  variety  in 
 the  ratio  of  1  :  1  :  2.  If  the  mixture  is 
 worth  ?153  per  kg,  then  the  price  of  the 
 third variety per kg (in  ?) is: 
 SSC CGL 21/07/2023 (2nd shift) 
 (a) 182.5  (b) 195.5   (c) 133.5  (d) 175.5 
 Q.63.  A  40  -  litre  mixture  contains  25% 
 alcohol  and  75%  water.  If  10  litres  of  water 
 are  added  to  the  mixture,  the  percentage  of 
 alcohol in the new mixture is: 
 SSC CGL 25/07/2023 (4th shift) 
 (a) 27%     (b) 18%     (c) 20%    (d) 25% 
 SSC Selection Post (Phase - XI) 
 Q.64.  If  36  litres  of  20%  milk  solution  is 
 mixed  with  48  litres  of  10%  milk  solution, 
 then  what  will  be  the  percentage 
 concentration  of  milk  in  the  ?nal 
 solution? 
 Higher Secondary 27/06/2023 (Shift - 3) 
 (a) 14.28%  (b) 15.48% 
 (c) 12.38%  (d) 13.36% 
 Q.65.  A  merchant  bought  two  qualities  of 
 rice  at  the  rate  of  Rs.120/kg  and 
 Rs.220/kg.  In  72kg  of  the  second  quality 
 rice,  how  much  rice  (in  kg)  of  the  ?rst 
 quality  should  be  mixed  so  that  the 
 resulting  mixture  may  be  sold  at  the  rate 
 of Rs.280/kg to earn a pro?t of 40% 
 Matriculation Level 27/06/2023 (Shift - 2) 
 (a) 20  (b) 22  (c) 15  (d) 18 
 SSC MTS 2022 Tier - 1 
 Q.66.  In  A  mixture  of  180  litres,  the  ratio 
 of  milk  and  water  is  5  :  1.  If  this  ratio  is  to 
 be  3  :  2,  then  ?nd  the  quantity  of  water  to 
 be further added ? ( in litres ) 
 SSC MTS 03/05/2023 (Afternoon) 
 (a) 66  (b) 70      (c) 88  (d) 72 
 Q.67.  There  are  three  cups  of  mixture  of 
 milk  and  water  in  ratio  4  :  5,  5  :  6,  9  :  7. 
 36  liters  of  ?rst  and  44  liters  of  second 
 cup  are  taken.  How  much  quantity  from 
 third  cup  is  to  be  taken  so  that  ?nal 
 mixture  from  the  three  cups  will  have 
 milk and water in ratio 1 : 1 ? ( in litres ) 
 SSC MTS 10/05/2023 (Afternoon) 
 (a) 32  (b) 64     (c) 54        (d) 60 
 Q.68.  In a 64 litres mixture , the alcohol 
 and  water  are  in  the  ratio  of  1  :  3 
 respectively.  32  litres  of  mixture  is  taken 
 off  and  replaced  with  16  litres  of  water. 
 What  is  the  new  ratio  of  alcohol  and 
 water respectively ? 
 SSC MTS 19/05/2023 (Evening) 
 (a) 1 : 5      (b) 5 : 12    (c) 2 : 7    (d) 3 : 10 
 Q.69.  135  kg  of  an  alloy  A  is  mixed  with 
 72  kg  of  alloy  B  to  get  a  new  alloy.  If  alloy 
 A  has  zinc  and  copper  in  the  ratio  4  :  5 
 and  alloy  B  has  zinc  and  copper  in  ratio  7 
 :  5,  then  what  is  the  weight  of  zinc  in  the 
 new alloy? 
 SSC MTS 13/06/2023 (Morning) 
 (a) 102 kg  (b) 115 kg  (c) 85 kg (d) 92 kg 
 Q.70.  One  liquid  contains  20%  of  acid  and 
 the  other  liquid  contain  30%  of  acid.  A  can 
 is  ?lled  with  7  parts  of  the  ?rst  liquid  and 
 3  parts  of  the  second  liquid.  The 
 percentage  of  the  acid  in  the  new  mixture 
 is : 
 SSC MTS 15/06/2023 (Morning) 
 (a) 13%  (b) 30%  (c) 14%  (d) 23% 
 Q.71.  Mixture  of  milk  and  water  in  three 
 bottles  of  equal  capacity  is  in  the  ratio  4  : 
 1,  4  :  3  and  1  :  2  respectively.  These  three 
 bottles  are  emptied  into  a  large  bottle. 
 What  will  be  the  ratio  of  milk  and  water 
 respectively in the large bottle? 
 SSC MTS 15/06/2023 (Morning) 
 (a) 179 : 136  (b) 152 : 165 
 (c) 198 : 175  (d) 133 : 145 
 Q.72.  The  alcohol  and  water  in  a  mixture 
 are  in  the  ratio  of  4  :  5  respectively.  20 
 litre  water  is  added  to  it.  If  the  ratio  of 
 alcohol  and  water  in  the  new  mixture  is  1 
 :  3  respectively,  then  what  is  the  total 
 quantity  of  the  alcohol  in  the  new 
 mixture? 
 SSC MTS 16/06/2023 (Morning) 
 (a)  litres  (b) 15 litres 
 80 
 7 
 (c)  litres  (d)  litres 
 60 
 7 
 90 
 11 
 Q.73.  The  ratio  of  spirit  and  water  in  two 
 mixtures  of  46  litres  and  50  litres  is  11  : 
 12  and  2  :  3  respectively.  Both  the 
 mixtures  are  mixed.  Find  the  ratio  of  the 
 spirit and water in the new mixture. 
 SSC MTS 16/06/2023 (Evening) 
 (a) 8 : 9  (b) 7 : 9  (c) 5 : 6  (d) 3 : 7 
 Q.74.  An  alloy  contains  copper,  zinc  and 
 nickel  in  the  ratio  of  3  :  2  :  5  respectively. 
 What  quantity  of  nickel  (in  kg)  must  be 
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 Pinnacle  Day: 54th  Mixture and Alligation 
 added  to  100  kg  of  this  alloy  to  have  the 
 new  ratio  of  copper,  zinc  and  nickel  3:2:6 
 respectively ? 
 SSC MTS 20/06/2023 (Afternoon) 
 (a) 20 kg   (b) 10 kg   (c) 8 kg   (d) 15 kg 
 Q.75.  The  ratio  of  copper  and  zinc  in 
 brass  is  7  :  3.  How  much  amount  of 
 copper will be there in 200 kg of brass? 
 SSC MTS 20/06/2023 (Evening) 
 (a) 60 kg (b) 120 kg  (c) 160 kg  (d) 140 kg 
 SSC CHSL 2022 Tier - 1 
 Q.76.  In  a  mixture,  milk  and  water  are  in 
 ratio  of  1  :  4.  Some  milk  is  added  to  the 
 mixture  because  of  which  ratio  of  milk 
 and  water  becomes  2  :  1.  How  much  milk 
 was  added  as  a  percentage  of  the  initial 
 mixture ? 
 SSC CHSL 10/03/2023 (3rd Shift) 
 (a) 140 % (b) 700 % (c) 240 % (d) 400 % 
 SSC CGL 2022 Tier - 2 
 Q.77.  40  litres  of  milk  are  kept  in  a 
 container.  4  litres  of  milk  were  removed 
 from  this  container  and  replaced  with 
 water.  This  procedure  was  performed 
 two  more  times.  How  much  milk  does 
 the container now hold? 
 SSC CGL Tier II (02/03/2023) 
 (a) 30 litres  (b) 34.23 litres 
 (c) 29.16 litres  (d) 32 litres 
 Q.78.  How  many  kilograms  of  rice 
 costing  Rs.60  per  kg  must  be  mixed  with 
 24  kg  of  rice  costing  Rs.42  per  kg  so  that 
 there  may  be  a  gain  of  12%  by  selling  the 
 mixture at Rs.56 per kg ? 
 SSC CGL Tier II (07/03/2023) 
 (a) 22 kg  (b) 20 kg (c) 19.2 kg (d) 21.2 kg 
 SSC CGL 2022 Tier - 1 
 Q.79.  A  can  of  water  and  milk  mixture 
 contains  60%  milk.  A  part  of  this  mixture 
 is  replaced  by  another  mixture  containing 
 50%  milk  and  the  percentage  of  milk  was 
 found  to  be  52%.  The  quantity  of  mixture 
 replaced is: 
 SSC CGL 13/12/2022 (2nd Shift) 
 (a)  (b)  (c)  (d) 
 1 
 5 
 3 
 5 
 4 
 5 
 2 
 5 
 Q.80.  P  and  Q  are  two  alloys  of 
 aluminium  and  copper.  The  ratios  of 
 aluminium  and  copper  in  P  and  Q  are  5  : 
 11  and  3  :  5,  respectively.  If  a  third  alloy  is 
 formed  by  mixing  alloys  P  and  Q  in  the 
 ratio  of  1  :  3,  then  aluminium  is  what 
 percentage  (rounded  off  to  the  nearest 
 integer) of the copper in the third alloy ? 
 SSC CGL 13/12/2022 (4th Shift) 
 (a) 63 Percent  (b) 52 Percent 
 (c) 48 Percent  (d) 56 Percent 
 SSC CGL 2021 Tier - 2 
 Q.81.  The  ratio  of  milk  to  water  in  a  100 
 litres  mixture  is  2  :  3.  10  liters  of  this 
 mixture  is  withdrawn  and  replaced  with 
 milk.  This  process  is  repeated  2  more 
 times.  What  is  the  percentage  of  milk  in 
 the ?nal mixture ? 
 SSC CGL Tier II (08/08/2022) 
 (a) 56.26 percent      (b) 54.27 percent 
 (c) 58.21 percent      (d) 51.24 percent 
 SSC MTS 2021 Tier - 1 
 Q.82.  A  container  contains  a  mixture  of 
 two  liquids,  A  and  B,  in  the  ratio  7  :  5.  If  9 
 liters  of  the  mixture  is  replaced  by  9  liters 
 of  liquid  B,  then  the  ratio  of  the  two 
 liquids  becomes  7  :  9.  How  much  of 
 liquid  A  was  there  in  the  container 
 initially ? 
 SSC MTS 05/07/2022 (Evening) 
 (a) 21 liters  (b) 35 liters 
 (c) 40 liters  (d) 19 liters 
 Q.83.  A  solution  of  45%  alcohol  is  mixed 
 with  a  solution  of  60%  alcohol  in  the  ratio 
 of  2  :  3.  In  what  ratio  should  the  resultant 
 solution be mixed with a 72% alcohol 
 solution to get a 66% alcohol solution? 
 SSC MTS 07/07/2022 (Morning) 
 (a) 4 : 7  (b) 1 : 3  (c) 1 : 2  (d) 2 : 3 
 Q.84.  An  alloy  contains  a  mixture  of  two 
 metals  X  and  Y  in  the  ratio  of  2  :  3.  The 
 second  alloy  contains  a  mixture  of  the 
 same  metals,  X  and  Y,  in  the  ratio  7  :  3.  In 
 what  ratio  should  the  ?rst  and  second 
 alloys  be  mixed  so  as  to  make  a  new 
 alloy containing 50% of metal X ? 
 SSC MTS 12/07/2022 (Afternoon) 
 (a) 3 : 4  (b) 3 : 1  (c) 5 : 6  (d) 2 : 1 
 Q.85.  of  4  kg  of  an  alloy  is  lead  and 
 1 
 2 
 rest  of  it  is  tin.  of  5  kg  of  another  alloy 
 1 
 6 
 is  lead  and  the  rest  of  it  is  tin.  Find  the 
 ratio  of  lead  and  tin  in  the  mixture  of  the 
 given quantities of these two alloys. 
 SSC MTS 14/07/2022 (Afternoon) 
 (a) 4 : 9  (b) 2 : 3  (c) 17 : 37  (d) 13 : 17 
 Q.86.  In  ‘x’  liters  of  a  solution  containing 
 40%  milk,  60  liters  of  water  is  added,  due 
 to  which  the  concentration  of  water 
 becomes 70%. Find ‘X’. 
 SSC MTS 18/07/2022 (Evening) 
 (a) 20  (b) 466  (c) 60  (d) 180 
 SSC CHSL 2021 Tier - 1 
 Q.87.  A  beaker  is  ?lled  with  a  liquid,  3 
 parts  of  which  are  water  and  7  parts 
 some  medicine.  What  part  of  the  mixture 
 should  be  replaced  with  water  so  that  the 
 resultant  mixture  has  water  and  medicine 
 in a ratio 1 : 1 ? 
 SSC CHSL 02/06/2022(Morning) 
 (a)  (b)  (c)  (d) 
 2 
 7 
 1 
 7 
 2 
 5 
 1 
 5 
 SSC CGL 2020 Tier - 2 
 Q.88.  A  vessel  contained  a  solution  of 
 acid  and  water,  in  which  water  was  64%. 
 Four  litres  of  the  solution  was  taken  out 
 of  the  vessel  and  the  same  quantity  of 
 water  was  added.  If  the  resulting  solution 
 contains  30%  acid,  the  quantity  (in  litres) 
 of  the  water  in  the  solution,  at  the 
 beginning in the vessel, was: 
 SSC CGL Tier II  (03/02/2022) 
 (a) 11.36  (b) 15.36   (c) 8.64   (d) 12.64 
 SSC MTS 2020 Tier - 1 
 Q.89.  A  liquid  of  900g  is  the  mixture  of 
 ?our,  sugar  and  butter.  In  this  solution 
 ?our  is  three  times  as  much  as  sugar  and 
 sugar  is  two  times  as  much  as  butter. 
 Find the quantity of ?our in grams. 
 SSC MTS 08/10/2021(Morning) 
 (a) 600    (b) 550       (c) 750       (d) 500 
 Q.90.  A  large  container  has  a  50  litre 
 mixture  of  juice  and  water  in  the  ratio  3  : 
 2.  To  this  ,  60  litre  juice  and  water 
 mixture  is  added,  which  has  a  juice  to 
 water  ratio  of  2  :  1.  After  this  ,  11  litres  of 
 the  solution  is  replaced  with  pure  juice. 
 What  is  the  ratio  of  water  to  juice  in  the 
 ?nal mixture ? 
 SSC MTS 11/10/2021 (Morning) 
 (a) 37 : 18  (b) 29 : 81 
 (c) 4 : 7  (d) 18 : 37 
 Q.91.  Kulbhushan  started  a  juice  (syrup  + 
 water)  counter.  Initially,  he  had  140  litres 
 of  juice  which  had  40%  water  in  it.  He 
 sold  30  litres  of  the  juice.  Then  he  added 
 equal  amounts  of  syrup  and  water.  Now 
 the  ratio  of  water  to  syrup  became  3  :  4. 
 What quantity of water was added? 
 SSC MTS 13/10/2021 (Afternoon) 
 (a) 24 litres  (b) 28 litres 
 (c) 26 litres  (d) 22 litres 
 SSC MTS 2019 Tier -  1 
 Q.92.  A  mixture  has  milk  and  water  in  the 
 ratio  (by  volume)  of  8  :  3.  If  3  litre  of 
 water  is  added  to  it,  then  the  new  ratio  of 
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