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Pinnacle Day: 49th - 52nd Ratio & Proportion
Ratio & Proportion
Key - points:-
1) What are antecedent and consequent?
In the form ; x is called the ?? : ??
antecedent and y is called consequent .
2) can also be written as ?? : ??
??
??
3) Duplicate ratio (square) :-
Duplicate ratio of x : y will be ??
2
: ??
2
4) Sub-duplicate Ratio (square root):-
Sub-duplicate Ratio of x : y will be ?? : ??
5) Triplicate Ratio (cube) :-
Triplicate ratio of x : y will be ??
3
: ??
3
6) Sub-triplicate Ratio (cube root)
Sub-triplicate Ratio of x : y will be
3
?? :
3
??
7) Inverse ratio :- x : y will be y : x
8) Compound Ratio : If two or more
ratios are given, then the antecedent of
one is multiplied with antecedent of the
other and respective consequents are
also multiplied.
If a : b, c : d and e : f are three ratios, then
their compound ratio will be .
??????
??????
9) 3
rd
Proportional:- 3
rd
proportion of a
and b i.e. a : b :: b : x ?
Then , x =
??
2
??
10) 4
th
Proportional: 4
th
proportional of a,
b and c i.e. a : b :: c : x
Then , x =
?? × ??
??
11) Componendo and dividendo rule:
If a : b :: c : d , Then ?
?? + ??
?? - ??
=
?? + ??
?? - ??
12) Mean Proportion : Mean proportion
of two numbers, a and b, is given by . ????
Partnership
Concept 1
The ratio of pro?ts of two or more
partners will be equal to the ratio of their
respective equivalent investment ratio.
Equivalent investment = (Amount
Invested) (Time for which the amount ×
is invested).
We will take some examples to
understand the concepts of partnership.
Example 1: A invests Rs. 10,000 and B
invests Rs. 20,000 for a period of 1 year
each. The pro?t, after 1 year will be
divided in the ratio:
= =
???????????? ???? ??
???????????? ???? ??
10000 × 12
20000 × 12
1
2
Example 2: A invests Rs.100 in a
business. After 6 months B joins with an
investment of Rs. 200. At the end of 1
year C joins with an investment of
Rs.100. What will be the ratio of pro?t
after 3 years?
Example 3: In the previous case if the
total pro?t after 3 years is 10,000. What
will be the share of A?
Share of A in total pro?t =
10,000 =
3
3 + 5 + 2
×
3
10
× 10000
? 3 × 1000 = 3000
Note: In case someone invests
in-between the total period of time, just
take care for what time an amount is
invested. Similarly there can be a case
when someone opts out in that case
also, the time for which the amount was
invested will be taken into consideration
and not the full period.
Concept 2
If = = = = K, where K is
??
??
??
??
??
??
??
??
constant . Then , K =
?? + ?? + ?? + ??
?? + ?? + ?? + ??
Example : = = K, Find the
1 + ??
2 - ??
9 - ??
3 + ??
value of K ?
Sol . :- K = = = 2
1 + ?? + 9 - ??
2 - ?? + 3 + ??
10
5
Concept 3
If two or three ratios are given , and we
have to ?nd an individual ratio of all of
them, then we take LCM of the common
entities and then balancing the common
entities ,we get the required ratio.
Example :- a : b = 3 : 4 , b : c = 6 : 7.
LCM of the common entities i.e b = (4, 6)
= 12
a : b = 3 : 4 ) × 3 = 9 : 12
b : c = 6 : 7 ) × 2 = 12 : 14
So, a : b : c = 9 : 12 : 14
Note : In case there are more than three
ratios given , then the LCM approach will
be tedious in ?nding the individual ratio
of the given entities.
Alternative method
If a : b = 2 : 3, b : c = 4 : 5
c : d = 6 : 7, d : e = 1 : 2
To understand this concept we will take
some examples
Example 1 : ?5600 is to be divided
among A, B, C & D in such a way that the
ratio of share of A : B is 1 : 2, B : C is 3 : 1
, C : D is 2 : 3, ?nd the share of A and B
taken together ?
Share of A : B = 1 : 2
Share of B : C = 3 : 1
Share of C : D = 2 : 3
A : B : C : D ?
1 × 3 × 2 : 2 × 3 × 2 : 2 × 1 × 2 : 2 × 1 × 3
= 6 : 12 : 4 : 6 or 3 : 6 : 2 : 3
Sum of the share of all of them = 3 + 6 +
2 + 3 = 14 unit
Total share of (A + B) = × 5600
6 + 3
14
= 9 × 400 = ?3600
Example 2 : Sum of ? x is divided among
A, B, C such that the ratio of the shares of
A and B is 6 : 7 and that of B and C is 3 :
2. If the difference of the share of A and
C is ?540 . Find the value of x
Share of A and B = 6 : 7
Share of B and C = 3 : 2
Ratio of the shares of A, B and C = 6 × 3 :
3 × 7 : 7 × 2 = 18 : 21: 14
Diff. of A and C = 18 - 14 = 4 unit, which
corresponds to ?540
Total share of A, B and C = 18 + 21 + 14
= 53 unit = × 53 = ? 7155
540
4
Concept 4
If numerator and denominator of a ratio
is multiplied and divided by same
number, the ratio remains unchanged .
E.g. :- = =
??
??
?? × ??
?? × ??
??
??
??
??
Ratio is independent of change in scale
only and not of origin.
Concept 5
If there is ‘n’ number of unequal fractions
such as , , , then
?? 1
?? 1
?? 2
?? 2
?? 3
?? 3
?? 4
?? 4
.....
????
????
the ratio of (a
1
+a
2
+a
3
+..a
n
) and (b
1
+ b
2
+
b
3
+ … b
n
) lies between lowest and
highest values of these fractions.
Example:- three unequal fractions are
1
2
, , . So, the ratio of (1 + 2 + 4) : (2 + 3
2
3
4
7
+ 7) = 7:12. Among these fractions,
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Page 2
Pinnacle Day: 49th - 52nd Ratio & Proportion
Ratio & Proportion
Key - points:-
1) What are antecedent and consequent?
In the form ; x is called the ?? : ??
antecedent and y is called consequent .
2) can also be written as ?? : ??
??
??
3) Duplicate ratio (square) :-
Duplicate ratio of x : y will be ??
2
: ??
2
4) Sub-duplicate Ratio (square root):-
Sub-duplicate Ratio of x : y will be ?? : ??
5) Triplicate Ratio (cube) :-
Triplicate ratio of x : y will be ??
3
: ??
3
6) Sub-triplicate Ratio (cube root)
Sub-triplicate Ratio of x : y will be
3
?? :
3
??
7) Inverse ratio :- x : y will be y : x
8) Compound Ratio : If two or more
ratios are given, then the antecedent of
one is multiplied with antecedent of the
other and respective consequents are
also multiplied.
If a : b, c : d and e : f are three ratios, then
their compound ratio will be .
??????
??????
9) 3
rd
Proportional:- 3
rd
proportion of a
and b i.e. a : b :: b : x ?
Then , x =
??
2
??
10) 4
th
Proportional: 4
th
proportional of a,
b and c i.e. a : b :: c : x
Then , x =
?? × ??
??
11) Componendo and dividendo rule:
If a : b :: c : d , Then ?
?? + ??
?? - ??
=
?? + ??
?? - ??
12) Mean Proportion : Mean proportion
of two numbers, a and b, is given by . ????
Partnership
Concept 1
The ratio of pro?ts of two or more
partners will be equal to the ratio of their
respective equivalent investment ratio.
Equivalent investment = (Amount
Invested) (Time for which the amount ×
is invested).
We will take some examples to
understand the concepts of partnership.
Example 1: A invests Rs. 10,000 and B
invests Rs. 20,000 for a period of 1 year
each. The pro?t, after 1 year will be
divided in the ratio:
= =
???????????? ???? ??
???????????? ???? ??
10000 × 12
20000 × 12
1
2
Example 2: A invests Rs.100 in a
business. After 6 months B joins with an
investment of Rs. 200. At the end of 1
year C joins with an investment of
Rs.100. What will be the ratio of pro?t
after 3 years?
Example 3: In the previous case if the
total pro?t after 3 years is 10,000. What
will be the share of A?
Share of A in total pro?t =
10,000 =
3
3 + 5 + 2
×
3
10
× 10000
? 3 × 1000 = 3000
Note: In case someone invests
in-between the total period of time, just
take care for what time an amount is
invested. Similarly there can be a case
when someone opts out in that case
also, the time for which the amount was
invested will be taken into consideration
and not the full period.
Concept 2
If = = = = K, where K is
??
??
??
??
??
??
??
??
constant . Then , K =
?? + ?? + ?? + ??
?? + ?? + ?? + ??
Example : = = K, Find the
1 + ??
2 - ??
9 - ??
3 + ??
value of K ?
Sol . :- K = = = 2
1 + ?? + 9 - ??
2 - ?? + 3 + ??
10
5
Concept 3
If two or three ratios are given , and we
have to ?nd an individual ratio of all of
them, then we take LCM of the common
entities and then balancing the common
entities ,we get the required ratio.
Example :- a : b = 3 : 4 , b : c = 6 : 7.
LCM of the common entities i.e b = (4, 6)
= 12
a : b = 3 : 4 ) × 3 = 9 : 12
b : c = 6 : 7 ) × 2 = 12 : 14
So, a : b : c = 9 : 12 : 14
Note : In case there are more than three
ratios given , then the LCM approach will
be tedious in ?nding the individual ratio
of the given entities.
Alternative method
If a : b = 2 : 3, b : c = 4 : 5
c : d = 6 : 7, d : e = 1 : 2
To understand this concept we will take
some examples
Example 1 : ?5600 is to be divided
among A, B, C & D in such a way that the
ratio of share of A : B is 1 : 2, B : C is 3 : 1
, C : D is 2 : 3, ?nd the share of A and B
taken together ?
Share of A : B = 1 : 2
Share of B : C = 3 : 1
Share of C : D = 2 : 3
A : B : C : D ?
1 × 3 × 2 : 2 × 3 × 2 : 2 × 1 × 2 : 2 × 1 × 3
= 6 : 12 : 4 : 6 or 3 : 6 : 2 : 3
Sum of the share of all of them = 3 + 6 +
2 + 3 = 14 unit
Total share of (A + B) = × 5600
6 + 3
14
= 9 × 400 = ?3600
Example 2 : Sum of ? x is divided among
A, B, C such that the ratio of the shares of
A and B is 6 : 7 and that of B and C is 3 :
2. If the difference of the share of A and
C is ?540 . Find the value of x
Share of A and B = 6 : 7
Share of B and C = 3 : 2
Ratio of the shares of A, B and C = 6 × 3 :
3 × 7 : 7 × 2 = 18 : 21: 14
Diff. of A and C = 18 - 14 = 4 unit, which
corresponds to ?540
Total share of A, B and C = 18 + 21 + 14
= 53 unit = × 53 = ? 7155
540
4
Concept 4
If numerator and denominator of a ratio
is multiplied and divided by same
number, the ratio remains unchanged .
E.g. :- = =
??
??
?? × ??
?? × ??
??
??
??
??
Ratio is independent of change in scale
only and not of origin.
Concept 5
If there is ‘n’ number of unequal fractions
such as , , , then
?? 1
?? 1
?? 2
?? 2
?? 3
?? 3
?? 4
?? 4
.....
????
????
the ratio of (a
1
+a
2
+a
3
+..a
n
) and (b
1
+ b
2
+
b
3
+ … b
n
) lies between lowest and
highest values of these fractions.
Example:- three unequal fractions are
1
2
, , . So, the ratio of (1 + 2 + 4) : (2 + 3
2
3
4
7
+ 7) = 7:12. Among these fractions,
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Pinnacle Day: 49th - 52nd Ratio & Proportion
lowest fraction is and the highest
1
2
fraction is so, the required value lies
2
3
between and .
1
2
2
3
Concept 6:
If aA = bB = cC, where a,b,c are constants
and A, B, C are variables. Then the ratio
of A : B : C = b × c : c × a : a × b.
Example: if 3A = 4B = 5C, then ?nd A:B:C
The ratio of A : B : C = 4 × 5 : 5 × 3 : 3 × 4
= 20 : 15 : 12
Variety Questions
Q.1. The concentration of three wines A,
B and C are 10%, 20% and 30%,
respectively. They are mixed in the ratio 2
: 3 : x resulting in a 23% concentration
solution. Find the value of x.
SSC CHSL Tier II 02/11/2023
(a) 7 (b) 6 (c) 8 (d) 5
Q.2. In a school of 720 students, the ratio
of boys to girls is 3 : 5. Find how many
new boys may be allowed to the school if
18 new girls are admitted, so that the
ratio of boys to girls changes to 2 : 3.
SSC CPO 05/10/2023 (3rd Shift)
(a) 42 (b) 50 (c) 44 (d) 38
Q.3. Ram has 12 hens and 5 cows,
Shyam has 18 hens and 9 cows,
Preetham has 4 hens and 8 cows, and
Vinay has 10 hens and 7 cows. Who has
a greater ratio of hens to cows?
SSC CPO 05/10/2023 (2nd Shift)
(a) Shyam (b) Preetham
(c) Vinay (d) Ram
Q.4. A company is manufacturing boxes
of three types - plastic, wood and glass.
The ratio of the numbers of plastic, wood
and glass boxes is 2 : 3 : 5. The
difference between the numbers of wood
and glass boxes is 144. If the number of
plastic boxes is increased by 25%, then
what will be the number of plastic boxes
now ?
SSC CPO 04/10/2023 (1st Shift)
(a) 144 (b) 216 (c) 360 (d) 180
Q.5. Find the fourth proportional of 12
35
,3
12
and 4
12
.
SSC MTS 14/09/2023 (3rd Shift)
(a) 12
-23
(b) 3
24
(c) 12
-11
(d) 4
24
Q.6. Three numbers are in the ratio 1 : 2 :
3. By adding 5 to each of the numbers
then the ratio changes to 2 : 3 : 4. The
smallest number is:
SSC MTS 14/09/2023 (1st Shift)
(a) 5 (b) 15 (c) 12 (d) 20
Q.7. When x = 1 then y is directly
proportional to x + 3 and y = 8. When z =
6 then x is inversely proportional to z and
x = 2. Find the relation between y and z.
SSC MTS 12/09/2023 (2nd Shift)
(a) (y - 6) / z = 24 (b) (y - 6) / z = 12
(c) z(y - 6) = 12 (d) z(y - 6) = 24
Q.8. The average of the two numbers is
48. If 3 is added to a smaller number,
then the ratio between them is 11 : 20.
Find the larger number. (Round up to two
decimal places).
SSC MTS 05/09/2023 (3rd Shift)
(a) 40.87 (b) 3.87 (c) 63.87 (d) 70.87
Q.9. Arrange the ratios in ascending
order 5 : 3 , 6 : 3 and 3.5 : 4.5.
1
3
1
4
1
8
SSC MTS 05/09/2023 (1st Shift)
(a) 3.5 : 4.5 < 5 : 3 < 6 : 3
1
3
1
4
1
8
(b) 6 : 3 < 5 : 3 < 3.5 : 4.5
1
4
1
8
1
3
(c) 5 : 3 < 3.5 : 4.5 < 6 : 3
1
3
1
4
1
8
(d) 5 : 3 < 6 : 3 < 3.5 : 4.5
1
3
1
4
1
8
Q.10. The incomes of P , Q and R are in
the ratio of 9 : 15 : 10 and their savings
are in the ratio is 10 : 15 : 12. If R spends
60% of his income, what is the ratio of
the expenditures of P , Q and R?
SSC MTS 05/09/2023 (1st Shift)
(a) 18 : 17 : 30 (b) 17 : 30 : 18
(c) 17 : 18 : 30 (d) 18 : 30 : 17
Q.11. Find the fourth proportional to
( ?? + ?? )
2
× ( ??
3
- ??
3
), ( ??
3
+ ??
3
), ( ??
2
- ??
2
).
SSC MTS 01/09/2023 (2nd Shift)
(a) (b)
( ??
2
- ???? + ??
2
)
( ?? + ?? )
( ??
2
+ ???? + ??
2
)
( ?? - ?? )
(c) (d)
( ??
2
- ???? + ??
2
)
( ??
2
+ ???? + ??
2
)
( ??
2
+ ???? + ??
2
)
( ??
2
- ??
2
)
Q.12. Two numbers A and B are such
that the sum of 6% of A and 4% of B is
2
5
of the sum of 7% of A and 11% of B, then
the ratio A : B is:
SSC MTS 01/09/2023 (1st Shift)
(a) 3 : 7 (b) 5 : 8 (c) 1 : 8 (d) 1 : 7
Q.13. A certain sum was to be divided
between A and B in the ratio 8 : 5.
However, by mistake, it was divided in the
ratio 5 : 8. Thus, A gets 300 less than ?
his original share. Find the sum.
SSC CHSL 17/08/2023 (4th Shift)
(a) ?2,600 (b) ?1,500 (c) ?1,300 (d) ?600
Q.14. When P is subtracted from each of
the numbers 8, 6, 2 and 9, the numbers so
obtained in this order are in proportion.
What is the mean proportional between
(3P - 6) and (9P - 4) ?
SSC CHSL 10/08/2023 (4th Shift)
(a) 26 (b) 28 (c) 29 (d) 24
Q.15. A man invests ?44,000 in some
shares in the ratio 1 : 4 : 5 which pay
dividends of 10%, 15% and 25% on his
investment for one year, respectively. His
total dividend income is:
SSC CHSL 07/08/2023 (1st Shift)
(a) ? 7,850 (b) ? 8,580
(c) ? 7,970 (d) ? 8,510
Q.16. A sum of money is divided among A,
B, C in the ratio 3 : 2 : 5, respectively. If the
share of C is ?300 more than B. then how
much more money will A get than B ?
SSC CHSL 03/08/2023 (1st Shift)
(a) ?150 (b) ?75 (c) ?100 (d) ?125
Q.17. The mean proportional of (a + b)
, (a - b) is: ( ?? - ?? )
3
( ?? + ?? )
3
SSC CGL 25/07/2023 (4th shift)
(a) (b) (a b) ( ?? + ?? )
2
( ?? - ?? )
2
( ?? + ?? )
2
-
(c) (a + b) (d) ( ?? - ?? )
2
??
2
- ??
2
Q.18. The seats for Mathematics, English
and Chemistry in a school are in the ratio
of 6 : 4 : 7. If these seats are increased
by 20%, 40% and 60%, respectively, the
ratio of the increased seats is:
SSC CGL 19/07/2023 (2nd shift)
(a) 9 : 7 : 8 (b) 9 : 7 : 14
(c) 1 : 2 : 3 (d) 7 : 9 : 14
Q.19. In a party hall, there are people in
blue and red dresses. The ratio of the
number of men in blue to the number of
women in red is 3 : 7. The ratio of men in
red to the number of women in blue is 2 :
1. If the ratio of the number of people in
blue to the number of people in red is 35 :
76, then what is the ratio of the number
of men to the number of women ?
SSC MTS 04/05/2023 (Morning)
(a) 47 : 51 (b) 40 : 43
(c) 62 : 57 (d) 52 : 59
Q.20. P's income is 250 percent of Q's
income and P's expenditure is 180
percent of Q's expenditure. If P's income
is 400 percent of Q's expenditure, then
what is the respective ratio of P's savings
and Q's savings?
SSC CHSL 17/03/2023 (3rd Shift)
(a) 8 : 3 (b) 11 : 3 (c) 11 : 5 (d) 5 : 2
Q.21. The number of units manufactured
by company A was 12500 units in 2019
and 10625 units in 2020. While in
company B, the production fell from
34000 units in 2019 to 30600 units in
2020. If X and Y are the percentage
decrease in the number of units
manufactured by company A and B
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Page 3
Pinnacle Day: 49th - 52nd Ratio & Proportion
Ratio & Proportion
Key - points:-
1) What are antecedent and consequent?
In the form ; x is called the ?? : ??
antecedent and y is called consequent .
2) can also be written as ?? : ??
??
??
3) Duplicate ratio (square) :-
Duplicate ratio of x : y will be ??
2
: ??
2
4) Sub-duplicate Ratio (square root):-
Sub-duplicate Ratio of x : y will be ?? : ??
5) Triplicate Ratio (cube) :-
Triplicate ratio of x : y will be ??
3
: ??
3
6) Sub-triplicate Ratio (cube root)
Sub-triplicate Ratio of x : y will be
3
?? :
3
??
7) Inverse ratio :- x : y will be y : x
8) Compound Ratio : If two or more
ratios are given, then the antecedent of
one is multiplied with antecedent of the
other and respective consequents are
also multiplied.
If a : b, c : d and e : f are three ratios, then
their compound ratio will be .
??????
??????
9) 3
rd
Proportional:- 3
rd
proportion of a
and b i.e. a : b :: b : x ?
Then , x =
??
2
??
10) 4
th
Proportional: 4
th
proportional of a,
b and c i.e. a : b :: c : x
Then , x =
?? × ??
??
11) Componendo and dividendo rule:
If a : b :: c : d , Then ?
?? + ??
?? - ??
=
?? + ??
?? - ??
12) Mean Proportion : Mean proportion
of two numbers, a and b, is given by . ????
Partnership
Concept 1
The ratio of pro?ts of two or more
partners will be equal to the ratio of their
respective equivalent investment ratio.
Equivalent investment = (Amount
Invested) (Time for which the amount ×
is invested).
We will take some examples to
understand the concepts of partnership.
Example 1: A invests Rs. 10,000 and B
invests Rs. 20,000 for a period of 1 year
each. The pro?t, after 1 year will be
divided in the ratio:
= =
???????????? ???? ??
???????????? ???? ??
10000 × 12
20000 × 12
1
2
Example 2: A invests Rs.100 in a
business. After 6 months B joins with an
investment of Rs. 200. At the end of 1
year C joins with an investment of
Rs.100. What will be the ratio of pro?t
after 3 years?
Example 3: In the previous case if the
total pro?t after 3 years is 10,000. What
will be the share of A?
Share of A in total pro?t =
10,000 =
3
3 + 5 + 2
×
3
10
× 10000
? 3 × 1000 = 3000
Note: In case someone invests
in-between the total period of time, just
take care for what time an amount is
invested. Similarly there can be a case
when someone opts out in that case
also, the time for which the amount was
invested will be taken into consideration
and not the full period.
Concept 2
If = = = = K, where K is
??
??
??
??
??
??
??
??
constant . Then , K =
?? + ?? + ?? + ??
?? + ?? + ?? + ??
Example : = = K, Find the
1 + ??
2 - ??
9 - ??
3 + ??
value of K ?
Sol . :- K = = = 2
1 + ?? + 9 - ??
2 - ?? + 3 + ??
10
5
Concept 3
If two or three ratios are given , and we
have to ?nd an individual ratio of all of
them, then we take LCM of the common
entities and then balancing the common
entities ,we get the required ratio.
Example :- a : b = 3 : 4 , b : c = 6 : 7.
LCM of the common entities i.e b = (4, 6)
= 12
a : b = 3 : 4 ) × 3 = 9 : 12
b : c = 6 : 7 ) × 2 = 12 : 14
So, a : b : c = 9 : 12 : 14
Note : In case there are more than three
ratios given , then the LCM approach will
be tedious in ?nding the individual ratio
of the given entities.
Alternative method
If a : b = 2 : 3, b : c = 4 : 5
c : d = 6 : 7, d : e = 1 : 2
To understand this concept we will take
some examples
Example 1 : ?5600 is to be divided
among A, B, C & D in such a way that the
ratio of share of A : B is 1 : 2, B : C is 3 : 1
, C : D is 2 : 3, ?nd the share of A and B
taken together ?
Share of A : B = 1 : 2
Share of B : C = 3 : 1
Share of C : D = 2 : 3
A : B : C : D ?
1 × 3 × 2 : 2 × 3 × 2 : 2 × 1 × 2 : 2 × 1 × 3
= 6 : 12 : 4 : 6 or 3 : 6 : 2 : 3
Sum of the share of all of them = 3 + 6 +
2 + 3 = 14 unit
Total share of (A + B) = × 5600
6 + 3
14
= 9 × 400 = ?3600
Example 2 : Sum of ? x is divided among
A, B, C such that the ratio of the shares of
A and B is 6 : 7 and that of B and C is 3 :
2. If the difference of the share of A and
C is ?540 . Find the value of x
Share of A and B = 6 : 7
Share of B and C = 3 : 2
Ratio of the shares of A, B and C = 6 × 3 :
3 × 7 : 7 × 2 = 18 : 21: 14
Diff. of A and C = 18 - 14 = 4 unit, which
corresponds to ?540
Total share of A, B and C = 18 + 21 + 14
= 53 unit = × 53 = ? 7155
540
4
Concept 4
If numerator and denominator of a ratio
is multiplied and divided by same
number, the ratio remains unchanged .
E.g. :- = =
??
??
?? × ??
?? × ??
??
??
??
??
Ratio is independent of change in scale
only and not of origin.
Concept 5
If there is ‘n’ number of unequal fractions
such as , , , then
?? 1
?? 1
?? 2
?? 2
?? 3
?? 3
?? 4
?? 4
.....
????
????
the ratio of (a
1
+a
2
+a
3
+..a
n
) and (b
1
+ b
2
+
b
3
+ … b
n
) lies between lowest and
highest values of these fractions.
Example:- three unequal fractions are
1
2
, , . So, the ratio of (1 + 2 + 4) : (2 + 3
2
3
4
7
+ 7) = 7:12. Among these fractions,
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Pinnacle Day: 49th - 52nd Ratio & Proportion
lowest fraction is and the highest
1
2
fraction is so, the required value lies
2
3
between and .
1
2
2
3
Concept 6:
If aA = bB = cC, where a,b,c are constants
and A, B, C are variables. Then the ratio
of A : B : C = b × c : c × a : a × b.
Example: if 3A = 4B = 5C, then ?nd A:B:C
The ratio of A : B : C = 4 × 5 : 5 × 3 : 3 × 4
= 20 : 15 : 12
Variety Questions
Q.1. The concentration of three wines A,
B and C are 10%, 20% and 30%,
respectively. They are mixed in the ratio 2
: 3 : x resulting in a 23% concentration
solution. Find the value of x.
SSC CHSL Tier II 02/11/2023
(a) 7 (b) 6 (c) 8 (d) 5
Q.2. In a school of 720 students, the ratio
of boys to girls is 3 : 5. Find how many
new boys may be allowed to the school if
18 new girls are admitted, so that the
ratio of boys to girls changes to 2 : 3.
SSC CPO 05/10/2023 (3rd Shift)
(a) 42 (b) 50 (c) 44 (d) 38
Q.3. Ram has 12 hens and 5 cows,
Shyam has 18 hens and 9 cows,
Preetham has 4 hens and 8 cows, and
Vinay has 10 hens and 7 cows. Who has
a greater ratio of hens to cows?
SSC CPO 05/10/2023 (2nd Shift)
(a) Shyam (b) Preetham
(c) Vinay (d) Ram
Q.4. A company is manufacturing boxes
of three types - plastic, wood and glass.
The ratio of the numbers of plastic, wood
and glass boxes is 2 : 3 : 5. The
difference between the numbers of wood
and glass boxes is 144. If the number of
plastic boxes is increased by 25%, then
what will be the number of plastic boxes
now ?
SSC CPO 04/10/2023 (1st Shift)
(a) 144 (b) 216 (c) 360 (d) 180
Q.5. Find the fourth proportional of 12
35
,3
12
and 4
12
.
SSC MTS 14/09/2023 (3rd Shift)
(a) 12
-23
(b) 3
24
(c) 12
-11
(d) 4
24
Q.6. Three numbers are in the ratio 1 : 2 :
3. By adding 5 to each of the numbers
then the ratio changes to 2 : 3 : 4. The
smallest number is:
SSC MTS 14/09/2023 (1st Shift)
(a) 5 (b) 15 (c) 12 (d) 20
Q.7. When x = 1 then y is directly
proportional to x + 3 and y = 8. When z =
6 then x is inversely proportional to z and
x = 2. Find the relation between y and z.
SSC MTS 12/09/2023 (2nd Shift)
(a) (y - 6) / z = 24 (b) (y - 6) / z = 12
(c) z(y - 6) = 12 (d) z(y - 6) = 24
Q.8. The average of the two numbers is
48. If 3 is added to a smaller number,
then the ratio between them is 11 : 20.
Find the larger number. (Round up to two
decimal places).
SSC MTS 05/09/2023 (3rd Shift)
(a) 40.87 (b) 3.87 (c) 63.87 (d) 70.87
Q.9. Arrange the ratios in ascending
order 5 : 3 , 6 : 3 and 3.5 : 4.5.
1
3
1
4
1
8
SSC MTS 05/09/2023 (1st Shift)
(a) 3.5 : 4.5 < 5 : 3 < 6 : 3
1
3
1
4
1
8
(b) 6 : 3 < 5 : 3 < 3.5 : 4.5
1
4
1
8
1
3
(c) 5 : 3 < 3.5 : 4.5 < 6 : 3
1
3
1
4
1
8
(d) 5 : 3 < 6 : 3 < 3.5 : 4.5
1
3
1
4
1
8
Q.10. The incomes of P , Q and R are in
the ratio of 9 : 15 : 10 and their savings
are in the ratio is 10 : 15 : 12. If R spends
60% of his income, what is the ratio of
the expenditures of P , Q and R?
SSC MTS 05/09/2023 (1st Shift)
(a) 18 : 17 : 30 (b) 17 : 30 : 18
(c) 17 : 18 : 30 (d) 18 : 30 : 17
Q.11. Find the fourth proportional to
( ?? + ?? )
2
× ( ??
3
- ??
3
), ( ??
3
+ ??
3
), ( ??
2
- ??
2
).
SSC MTS 01/09/2023 (2nd Shift)
(a) (b)
( ??
2
- ???? + ??
2
)
( ?? + ?? )
( ??
2
+ ???? + ??
2
)
( ?? - ?? )
(c) (d)
( ??
2
- ???? + ??
2
)
( ??
2
+ ???? + ??
2
)
( ??
2
+ ???? + ??
2
)
( ??
2
- ??
2
)
Q.12. Two numbers A and B are such
that the sum of 6% of A and 4% of B is
2
5
of the sum of 7% of A and 11% of B, then
the ratio A : B is:
SSC MTS 01/09/2023 (1st Shift)
(a) 3 : 7 (b) 5 : 8 (c) 1 : 8 (d) 1 : 7
Q.13. A certain sum was to be divided
between A and B in the ratio 8 : 5.
However, by mistake, it was divided in the
ratio 5 : 8. Thus, A gets 300 less than ?
his original share. Find the sum.
SSC CHSL 17/08/2023 (4th Shift)
(a) ?2,600 (b) ?1,500 (c) ?1,300 (d) ?600
Q.14. When P is subtracted from each of
the numbers 8, 6, 2 and 9, the numbers so
obtained in this order are in proportion.
What is the mean proportional between
(3P - 6) and (9P - 4) ?
SSC CHSL 10/08/2023 (4th Shift)
(a) 26 (b) 28 (c) 29 (d) 24
Q.15. A man invests ?44,000 in some
shares in the ratio 1 : 4 : 5 which pay
dividends of 10%, 15% and 25% on his
investment for one year, respectively. His
total dividend income is:
SSC CHSL 07/08/2023 (1st Shift)
(a) ? 7,850 (b) ? 8,580
(c) ? 7,970 (d) ? 8,510
Q.16. A sum of money is divided among A,
B, C in the ratio 3 : 2 : 5, respectively. If the
share of C is ?300 more than B. then how
much more money will A get than B ?
SSC CHSL 03/08/2023 (1st Shift)
(a) ?150 (b) ?75 (c) ?100 (d) ?125
Q.17. The mean proportional of (a + b)
, (a - b) is: ( ?? - ?? )
3
( ?? + ?? )
3
SSC CGL 25/07/2023 (4th shift)
(a) (b) (a b) ( ?? + ?? )
2
( ?? - ?? )
2
( ?? + ?? )
2
-
(c) (a + b) (d) ( ?? - ?? )
2
??
2
- ??
2
Q.18. The seats for Mathematics, English
and Chemistry in a school are in the ratio
of 6 : 4 : 7. If these seats are increased
by 20%, 40% and 60%, respectively, the
ratio of the increased seats is:
SSC CGL 19/07/2023 (2nd shift)
(a) 9 : 7 : 8 (b) 9 : 7 : 14
(c) 1 : 2 : 3 (d) 7 : 9 : 14
Q.19. In a party hall, there are people in
blue and red dresses. The ratio of the
number of men in blue to the number of
women in red is 3 : 7. The ratio of men in
red to the number of women in blue is 2 :
1. If the ratio of the number of people in
blue to the number of people in red is 35 :
76, then what is the ratio of the number
of men to the number of women ?
SSC MTS 04/05/2023 (Morning)
(a) 47 : 51 (b) 40 : 43
(c) 62 : 57 (d) 52 : 59
Q.20. P's income is 250 percent of Q's
income and P's expenditure is 180
percent of Q's expenditure. If P's income
is 400 percent of Q's expenditure, then
what is the respective ratio of P's savings
and Q's savings?
SSC CHSL 17/03/2023 (3rd Shift)
(a) 8 : 3 (b) 11 : 3 (c) 11 : 5 (d) 5 : 2
Q.21. The number of units manufactured
by company A was 12500 units in 2019
and 10625 units in 2020. While in
company B, the production fell from
34000 units in 2019 to 30600 units in
2020. If X and Y are the percentage
decrease in the number of units
manufactured by company A and B
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Pinnacle Day: 49th - 52nd Ratio & Proportion
respectively from 2019 to 2020, then
what will be the ratio of X and Y?
SSC CGL 13/12/2022 (1st Shift)
(a) 5 : 3 (b) 3 : 4 (c) 3 : 2 (d) 8 : 5
Q.22. Find the mean proportion of
and .
??
3
+ ??
3
?? - ??
??
2
- ??
2
??
2
- ???? + ??
2
SSC CGL 06/12/2022 (3rd Shift)
(a) 1 (b) a + b (c) (d)
?? + ??
?? - ??
?? + ??
Q.23. In an o?ce with 40 o?cers, the
average salaries of class-A, class-B and
class-C o?cers are ?600, ?750 and
?1,000 a day, respectively. The number of
class-A, class-B and class-C o?cers in
the o?ce are in the ratio 5 : 4 : 1,
respectively. Find the monthly average
salary (in ?) of an o?cers, all the 40 of
them taken together. [Assume the
number of days in a month to be 30.]
SSC MTS 08/07/2022 (Morning)
(a) 25,800 (b) 21,000
(c) 24,030 (d) 24,600
Q.24. The ratio of income of A to that of
B is 4 : 3. The expenditure of A is of
5
12
his income and the expenditure of B is
of his income. The difference
7
15
between their expenditure is ?4,500. Find
the income of B.
SSC CHSL 25/05/2022 (Evening)
(a) ?49,625 (b) ?48,625
(c) ?51,625 (d) ?50,625
Q.25. A sum of ?46,800 is divided among
A, B, C and D in such a way that the ratio
of the combined share of A and D to the
combined share of B and C is 8 : 5. The
ratio of the share of B to that of C is 5: 4.
A receives ?18,400. If x is the difference
between the shares of A and B and y is
the difference between the shares of C
and D, then what is the value of (x - y) (in
?) ?
SSC CGL Tier II (29/01/2022)
(a) 6000 (b) 6500 (c) 5000 (d) 7000
Q.26. If a number of pens and pencils are
bought in the ratio of 5 : 3, then Ashok
has to pay ?44. If the ratio is changed as
3 : 5, then he has to pay ?36. Find the
ratio of the price of one pen to one
pencil.
SSC MTS 11/10/2021 (Evening)
(a) 5 : 3 (b) 7 : 3 (c) 8 : 5 (d) 7 : 4
Q.27. Atul purchased Bread costing
Rs.20 and gave a 100 rupee note to the
shopkeeper. The shopkeeper gave the
balance money in coins of denomination
2, 5, and 10. If these coins are in the ratio
5 : 4 : 1, then how many 5 coins did the
shopkeeper give?
SSC CGL 03/08/2021 (Evening)
(a) 5 (b) 6 (c) 8 (d) 4
Q.28. In a school, of the number of
3
8
students are girls and the rest are boys,
One - third of the number of boys are
below 10 years and of the number of
2
3
girls is also below 10 years. If the
number of students of age 10 or more
years is 260, then the number of boys in
the school is:
SSC CGL Tier II (15/11/2020)
(a) 280 (b) 300 (c) 234 (d) 312
Q.29. By adding 3 and 5 in numerator
and denominator of a fraction it
becomes . If 1 and 3 are subtracted
2
3
and added from numerator and
denominator respectively, it becomes .
2
5
Find the fraction.
SSC CHSL 19/10/2020 (Morning shift)
(a) (b) (c) (d)
5
7
6
7
7
6
7
5
Q.30. A, B and C spend 80%, 85% and
75% of their incomes, respectively. If
their savings are in the ratio 8 : 9 : 20 and
the difference between the incomes of A
and C is Rs. 18,000 , then the income of
B is :
SSC CGL Tier II (13/09/2019)
(a) Rs. 24,000 (b) Rs. 27,000
(c) Rs. 30,000 (d) Rs. 36,000
Q.31. The ratio of income of A and B last
year was 4 : 3, respectively. The ratios of
their individual incomes of the last year
and the present year are 3 : 4 and 5 : 6,
respectively. If their total income for the
present year is Rs. 8.04 lakh, then the
income of B last year was :
SSC CGL Tier II (12/09/2019)
(a) Rs. 2.7 lakh (b) Rs. 3.6 lakh
(c) Rs. 2.4 lakh (d) Rs. 2.8 lakh
Q.32. The ratio of the income of A to that
of B is 5 : 7. A and B save Rs. 4000 and
Rs. 5000 respectively. If the expenditure
of A is equal to 66 % of the expenditure
2
3
of B, then the total income of A and B is :
SSC CGL Tier II (11/09/2019)
(a) Rs. 25,200 (b) Rs. 24,000
(c) Rs. 26,400 (d) Rs. 28,800
Q.33. The ratio between the divisor and
remainder is 3 : 2 and the ratio between
the divisor and the quotient is 7 : 12. If
the remainder is 14, then ?nd the
remainder when the dividend is divided
by 9.
SSC MTS 21/08/2019 (Morning)
(a) 3 (b) 6 (c) 4 (d) 5
Q.34. Ravi’s age is of Shyam’s age.
3
5
After x years the ratio of the ages of Ravi
and Shyam becomes 5 : 7. If initially the
sum of their ages is 32, then what is the
value of x ?
SSC MTS 08/08/2019 (Morning)
(a) 2 (b) 4 (c) 8 (d) 7
Q.35. What is the ratio between the
fourth proportional of 3, 4, 9 and the
mean proportional between 2 and 98?
SSC CHSL 11/07/2019 (Afternoon)
(a) 7 : 8 (b) 7 : 6 (c) 8 : 7 (d) 6 : 7
Q.36. Rs. 8000 is distributed among A, B
and C such that they receive notes of Rs.
500, Rs. 200 and Rs. 100 respectively.
The amounts received by them are in the
ratio 15 : 2 : 3. What was the ratio of the
numbers of notes of Rs. 500, Rs 200 and
Rs 100 ?
SSC CHSL 10/07/2019 (Morning)
(a) 3:1:3 (b) 3:3:1 (c) 4:1:2 (d) 3:2:2
Q.37. The ratio of incomes of A and B is
2 : 3 and that of their expenditure is 1 : 2.
If 90% of B’s expenditure is equal to the
income of A , then what is the ratio of the
savings of A and B?
SSC CHSL 02/07/2019 (Morning)
(a) 1 : 1 (b) 9 : 8 (c) 8 : 7 (d) 3 : 2
Q.38. A sum of Rs. 4360 was to be
divided among A , B , C and D in the ratio
of 3 : 4 : 5 : 8, but it was divided in the
ratio of : : : by mistake.
1
3
1
4
1
5
1
8
As a result:
SSC CHSL 01/07/2019 (Evening)
(a) A received Rs. 956 more
(b) B received Rs. 318 more
(c) D received Rs. 1144 less
(d) C received Rs. 132 less
Q.39. If a : b = 2 : 5 , c : b = 3 : 4 , then a :
b : c is equal to :
SSC CGL 12/06/2019 (Evening)
(a) 6 : 15 : 20 (b) 8 : 20 : 15
(c) 2 : 5 : 4 (d) 2 : 5 : 3
Q.40. A sum of Rs. x is divided among A ,
B and C such that the ratio of shares of A
and B is 7 : 12 and that of B and C is 8 : 5.
If the difference in the shares of A and C
is Rs. 214 , then the value of x is :
SSC CGL 07/06/2019 (Evening)
(a) 11556 (b) 11128 (c) 11770 (d) 11342
Q.41. The prices of two articles are in the
ratio 4 : 5. If the price of the ?rst article is
increased by x% and that of the other is
decreased by 30% , then the new prices
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Page 4
Pinnacle Day: 49th - 52nd Ratio & Proportion
Ratio & Proportion
Key - points:-
1) What are antecedent and consequent?
In the form ; x is called the ?? : ??
antecedent and y is called consequent .
2) can also be written as ?? : ??
??
??
3) Duplicate ratio (square) :-
Duplicate ratio of x : y will be ??
2
: ??
2
4) Sub-duplicate Ratio (square root):-
Sub-duplicate Ratio of x : y will be ?? : ??
5) Triplicate Ratio (cube) :-
Triplicate ratio of x : y will be ??
3
: ??
3
6) Sub-triplicate Ratio (cube root)
Sub-triplicate Ratio of x : y will be
3
?? :
3
??
7) Inverse ratio :- x : y will be y : x
8) Compound Ratio : If two or more
ratios are given, then the antecedent of
one is multiplied with antecedent of the
other and respective consequents are
also multiplied.
If a : b, c : d and e : f are three ratios, then
their compound ratio will be .
??????
??????
9) 3
rd
Proportional:- 3
rd
proportion of a
and b i.e. a : b :: b : x ?
Then , x =
??
2
??
10) 4
th
Proportional: 4
th
proportional of a,
b and c i.e. a : b :: c : x
Then , x =
?? × ??
??
11) Componendo and dividendo rule:
If a : b :: c : d , Then ?
?? + ??
?? - ??
=
?? + ??
?? - ??
12) Mean Proportion : Mean proportion
of two numbers, a and b, is given by . ????
Partnership
Concept 1
The ratio of pro?ts of two or more
partners will be equal to the ratio of their
respective equivalent investment ratio.
Equivalent investment = (Amount
Invested) (Time for which the amount ×
is invested).
We will take some examples to
understand the concepts of partnership.
Example 1: A invests Rs. 10,000 and B
invests Rs. 20,000 for a period of 1 year
each. The pro?t, after 1 year will be
divided in the ratio:
= =
???????????? ???? ??
???????????? ???? ??
10000 × 12
20000 × 12
1
2
Example 2: A invests Rs.100 in a
business. After 6 months B joins with an
investment of Rs. 200. At the end of 1
year C joins with an investment of
Rs.100. What will be the ratio of pro?t
after 3 years?
Example 3: In the previous case if the
total pro?t after 3 years is 10,000. What
will be the share of A?
Share of A in total pro?t =
10,000 =
3
3 + 5 + 2
×
3
10
× 10000
? 3 × 1000 = 3000
Note: In case someone invests
in-between the total period of time, just
take care for what time an amount is
invested. Similarly there can be a case
when someone opts out in that case
also, the time for which the amount was
invested will be taken into consideration
and not the full period.
Concept 2
If = = = = K, where K is
??
??
??
??
??
??
??
??
constant . Then , K =
?? + ?? + ?? + ??
?? + ?? + ?? + ??
Example : = = K, Find the
1 + ??
2 - ??
9 - ??
3 + ??
value of K ?
Sol . :- K = = = 2
1 + ?? + 9 - ??
2 - ?? + 3 + ??
10
5
Concept 3
If two or three ratios are given , and we
have to ?nd an individual ratio of all of
them, then we take LCM of the common
entities and then balancing the common
entities ,we get the required ratio.
Example :- a : b = 3 : 4 , b : c = 6 : 7.
LCM of the common entities i.e b = (4, 6)
= 12
a : b = 3 : 4 ) × 3 = 9 : 12
b : c = 6 : 7 ) × 2 = 12 : 14
So, a : b : c = 9 : 12 : 14
Note : In case there are more than three
ratios given , then the LCM approach will
be tedious in ?nding the individual ratio
of the given entities.
Alternative method
If a : b = 2 : 3, b : c = 4 : 5
c : d = 6 : 7, d : e = 1 : 2
To understand this concept we will take
some examples
Example 1 : ?5600 is to be divided
among A, B, C & D in such a way that the
ratio of share of A : B is 1 : 2, B : C is 3 : 1
, C : D is 2 : 3, ?nd the share of A and B
taken together ?
Share of A : B = 1 : 2
Share of B : C = 3 : 1
Share of C : D = 2 : 3
A : B : C : D ?
1 × 3 × 2 : 2 × 3 × 2 : 2 × 1 × 2 : 2 × 1 × 3
= 6 : 12 : 4 : 6 or 3 : 6 : 2 : 3
Sum of the share of all of them = 3 + 6 +
2 + 3 = 14 unit
Total share of (A + B) = × 5600
6 + 3
14
= 9 × 400 = ?3600
Example 2 : Sum of ? x is divided among
A, B, C such that the ratio of the shares of
A and B is 6 : 7 and that of B and C is 3 :
2. If the difference of the share of A and
C is ?540 . Find the value of x
Share of A and B = 6 : 7
Share of B and C = 3 : 2
Ratio of the shares of A, B and C = 6 × 3 :
3 × 7 : 7 × 2 = 18 : 21: 14
Diff. of A and C = 18 - 14 = 4 unit, which
corresponds to ?540
Total share of A, B and C = 18 + 21 + 14
= 53 unit = × 53 = ? 7155
540
4
Concept 4
If numerator and denominator of a ratio
is multiplied and divided by same
number, the ratio remains unchanged .
E.g. :- = =
??
??
?? × ??
?? × ??
??
??
??
??
Ratio is independent of change in scale
only and not of origin.
Concept 5
If there is ‘n’ number of unequal fractions
such as , , , then
?? 1
?? 1
?? 2
?? 2
?? 3
?? 3
?? 4
?? 4
.....
????
????
the ratio of (a
1
+a
2
+a
3
+..a
n
) and (b
1
+ b
2
+
b
3
+ … b
n
) lies between lowest and
highest values of these fractions.
Example:- three unequal fractions are
1
2
, , . So, the ratio of (1 + 2 + 4) : (2 + 3
2
3
4
7
+ 7) = 7:12. Among these fractions,
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Pinnacle Day: 49th - 52nd Ratio & Proportion
lowest fraction is and the highest
1
2
fraction is so, the required value lies
2
3
between and .
1
2
2
3
Concept 6:
If aA = bB = cC, where a,b,c are constants
and A, B, C are variables. Then the ratio
of A : B : C = b × c : c × a : a × b.
Example: if 3A = 4B = 5C, then ?nd A:B:C
The ratio of A : B : C = 4 × 5 : 5 × 3 : 3 × 4
= 20 : 15 : 12
Variety Questions
Q.1. The concentration of three wines A,
B and C are 10%, 20% and 30%,
respectively. They are mixed in the ratio 2
: 3 : x resulting in a 23% concentration
solution. Find the value of x.
SSC CHSL Tier II 02/11/2023
(a) 7 (b) 6 (c) 8 (d) 5
Q.2. In a school of 720 students, the ratio
of boys to girls is 3 : 5. Find how many
new boys may be allowed to the school if
18 new girls are admitted, so that the
ratio of boys to girls changes to 2 : 3.
SSC CPO 05/10/2023 (3rd Shift)
(a) 42 (b) 50 (c) 44 (d) 38
Q.3. Ram has 12 hens and 5 cows,
Shyam has 18 hens and 9 cows,
Preetham has 4 hens and 8 cows, and
Vinay has 10 hens and 7 cows. Who has
a greater ratio of hens to cows?
SSC CPO 05/10/2023 (2nd Shift)
(a) Shyam (b) Preetham
(c) Vinay (d) Ram
Q.4. A company is manufacturing boxes
of three types - plastic, wood and glass.
The ratio of the numbers of plastic, wood
and glass boxes is 2 : 3 : 5. The
difference between the numbers of wood
and glass boxes is 144. If the number of
plastic boxes is increased by 25%, then
what will be the number of plastic boxes
now ?
SSC CPO 04/10/2023 (1st Shift)
(a) 144 (b) 216 (c) 360 (d) 180
Q.5. Find the fourth proportional of 12
35
,3
12
and 4
12
.
SSC MTS 14/09/2023 (3rd Shift)
(a) 12
-23
(b) 3
24
(c) 12
-11
(d) 4
24
Q.6. Three numbers are in the ratio 1 : 2 :
3. By adding 5 to each of the numbers
then the ratio changes to 2 : 3 : 4. The
smallest number is:
SSC MTS 14/09/2023 (1st Shift)
(a) 5 (b) 15 (c) 12 (d) 20
Q.7. When x = 1 then y is directly
proportional to x + 3 and y = 8. When z =
6 then x is inversely proportional to z and
x = 2. Find the relation between y and z.
SSC MTS 12/09/2023 (2nd Shift)
(a) (y - 6) / z = 24 (b) (y - 6) / z = 12
(c) z(y - 6) = 12 (d) z(y - 6) = 24
Q.8. The average of the two numbers is
48. If 3 is added to a smaller number,
then the ratio between them is 11 : 20.
Find the larger number. (Round up to two
decimal places).
SSC MTS 05/09/2023 (3rd Shift)
(a) 40.87 (b) 3.87 (c) 63.87 (d) 70.87
Q.9. Arrange the ratios in ascending
order 5 : 3 , 6 : 3 and 3.5 : 4.5.
1
3
1
4
1
8
SSC MTS 05/09/2023 (1st Shift)
(a) 3.5 : 4.5 < 5 : 3 < 6 : 3
1
3
1
4
1
8
(b) 6 : 3 < 5 : 3 < 3.5 : 4.5
1
4
1
8
1
3
(c) 5 : 3 < 3.5 : 4.5 < 6 : 3
1
3
1
4
1
8
(d) 5 : 3 < 6 : 3 < 3.5 : 4.5
1
3
1
4
1
8
Q.10. The incomes of P , Q and R are in
the ratio of 9 : 15 : 10 and their savings
are in the ratio is 10 : 15 : 12. If R spends
60% of his income, what is the ratio of
the expenditures of P , Q and R?
SSC MTS 05/09/2023 (1st Shift)
(a) 18 : 17 : 30 (b) 17 : 30 : 18
(c) 17 : 18 : 30 (d) 18 : 30 : 17
Q.11. Find the fourth proportional to
( ?? + ?? )
2
× ( ??
3
- ??
3
), ( ??
3
+ ??
3
), ( ??
2
- ??
2
).
SSC MTS 01/09/2023 (2nd Shift)
(a) (b)
( ??
2
- ???? + ??
2
)
( ?? + ?? )
( ??
2
+ ???? + ??
2
)
( ?? - ?? )
(c) (d)
( ??
2
- ???? + ??
2
)
( ??
2
+ ???? + ??
2
)
( ??
2
+ ???? + ??
2
)
( ??
2
- ??
2
)
Q.12. Two numbers A and B are such
that the sum of 6% of A and 4% of B is
2
5
of the sum of 7% of A and 11% of B, then
the ratio A : B is:
SSC MTS 01/09/2023 (1st Shift)
(a) 3 : 7 (b) 5 : 8 (c) 1 : 8 (d) 1 : 7
Q.13. A certain sum was to be divided
between A and B in the ratio 8 : 5.
However, by mistake, it was divided in the
ratio 5 : 8. Thus, A gets 300 less than ?
his original share. Find the sum.
SSC CHSL 17/08/2023 (4th Shift)
(a) ?2,600 (b) ?1,500 (c) ?1,300 (d) ?600
Q.14. When P is subtracted from each of
the numbers 8, 6, 2 and 9, the numbers so
obtained in this order are in proportion.
What is the mean proportional between
(3P - 6) and (9P - 4) ?
SSC CHSL 10/08/2023 (4th Shift)
(a) 26 (b) 28 (c) 29 (d) 24
Q.15. A man invests ?44,000 in some
shares in the ratio 1 : 4 : 5 which pay
dividends of 10%, 15% and 25% on his
investment for one year, respectively. His
total dividend income is:
SSC CHSL 07/08/2023 (1st Shift)
(a) ? 7,850 (b) ? 8,580
(c) ? 7,970 (d) ? 8,510
Q.16. A sum of money is divided among A,
B, C in the ratio 3 : 2 : 5, respectively. If the
share of C is ?300 more than B. then how
much more money will A get than B ?
SSC CHSL 03/08/2023 (1st Shift)
(a) ?150 (b) ?75 (c) ?100 (d) ?125
Q.17. The mean proportional of (a + b)
, (a - b) is: ( ?? - ?? )
3
( ?? + ?? )
3
SSC CGL 25/07/2023 (4th shift)
(a) (b) (a b) ( ?? + ?? )
2
( ?? - ?? )
2
( ?? + ?? )
2
-
(c) (a + b) (d) ( ?? - ?? )
2
??
2
- ??
2
Q.18. The seats for Mathematics, English
and Chemistry in a school are in the ratio
of 6 : 4 : 7. If these seats are increased
by 20%, 40% and 60%, respectively, the
ratio of the increased seats is:
SSC CGL 19/07/2023 (2nd shift)
(a) 9 : 7 : 8 (b) 9 : 7 : 14
(c) 1 : 2 : 3 (d) 7 : 9 : 14
Q.19. In a party hall, there are people in
blue and red dresses. The ratio of the
number of men in blue to the number of
women in red is 3 : 7. The ratio of men in
red to the number of women in blue is 2 :
1. If the ratio of the number of people in
blue to the number of people in red is 35 :
76, then what is the ratio of the number
of men to the number of women ?
SSC MTS 04/05/2023 (Morning)
(a) 47 : 51 (b) 40 : 43
(c) 62 : 57 (d) 52 : 59
Q.20. P's income is 250 percent of Q's
income and P's expenditure is 180
percent of Q's expenditure. If P's income
is 400 percent of Q's expenditure, then
what is the respective ratio of P's savings
and Q's savings?
SSC CHSL 17/03/2023 (3rd Shift)
(a) 8 : 3 (b) 11 : 3 (c) 11 : 5 (d) 5 : 2
Q.21. The number of units manufactured
by company A was 12500 units in 2019
and 10625 units in 2020. While in
company B, the production fell from
34000 units in 2019 to 30600 units in
2020. If X and Y are the percentage
decrease in the number of units
manufactured by company A and B
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Pinnacle Day: 49th - 52nd Ratio & Proportion
respectively from 2019 to 2020, then
what will be the ratio of X and Y?
SSC CGL 13/12/2022 (1st Shift)
(a) 5 : 3 (b) 3 : 4 (c) 3 : 2 (d) 8 : 5
Q.22. Find the mean proportion of
and .
??
3
+ ??
3
?? - ??
??
2
- ??
2
??
2
- ???? + ??
2
SSC CGL 06/12/2022 (3rd Shift)
(a) 1 (b) a + b (c) (d)
?? + ??
?? - ??
?? + ??
Q.23. In an o?ce with 40 o?cers, the
average salaries of class-A, class-B and
class-C o?cers are ?600, ?750 and
?1,000 a day, respectively. The number of
class-A, class-B and class-C o?cers in
the o?ce are in the ratio 5 : 4 : 1,
respectively. Find the monthly average
salary (in ?) of an o?cers, all the 40 of
them taken together. [Assume the
number of days in a month to be 30.]
SSC MTS 08/07/2022 (Morning)
(a) 25,800 (b) 21,000
(c) 24,030 (d) 24,600
Q.24. The ratio of income of A to that of
B is 4 : 3. The expenditure of A is of
5
12
his income and the expenditure of B is
of his income. The difference
7
15
between their expenditure is ?4,500. Find
the income of B.
SSC CHSL 25/05/2022 (Evening)
(a) ?49,625 (b) ?48,625
(c) ?51,625 (d) ?50,625
Q.25. A sum of ?46,800 is divided among
A, B, C and D in such a way that the ratio
of the combined share of A and D to the
combined share of B and C is 8 : 5. The
ratio of the share of B to that of C is 5: 4.
A receives ?18,400. If x is the difference
between the shares of A and B and y is
the difference between the shares of C
and D, then what is the value of (x - y) (in
?) ?
SSC CGL Tier II (29/01/2022)
(a) 6000 (b) 6500 (c) 5000 (d) 7000
Q.26. If a number of pens and pencils are
bought in the ratio of 5 : 3, then Ashok
has to pay ?44. If the ratio is changed as
3 : 5, then he has to pay ?36. Find the
ratio of the price of one pen to one
pencil.
SSC MTS 11/10/2021 (Evening)
(a) 5 : 3 (b) 7 : 3 (c) 8 : 5 (d) 7 : 4
Q.27. Atul purchased Bread costing
Rs.20 and gave a 100 rupee note to the
shopkeeper. The shopkeeper gave the
balance money in coins of denomination
2, 5, and 10. If these coins are in the ratio
5 : 4 : 1, then how many 5 coins did the
shopkeeper give?
SSC CGL 03/08/2021 (Evening)
(a) 5 (b) 6 (c) 8 (d) 4
Q.28. In a school, of the number of
3
8
students are girls and the rest are boys,
One - third of the number of boys are
below 10 years and of the number of
2
3
girls is also below 10 years. If the
number of students of age 10 or more
years is 260, then the number of boys in
the school is:
SSC CGL Tier II (15/11/2020)
(a) 280 (b) 300 (c) 234 (d) 312
Q.29. By adding 3 and 5 in numerator
and denominator of a fraction it
becomes . If 1 and 3 are subtracted
2
3
and added from numerator and
denominator respectively, it becomes .
2
5
Find the fraction.
SSC CHSL 19/10/2020 (Morning shift)
(a) (b) (c) (d)
5
7
6
7
7
6
7
5
Q.30. A, B and C spend 80%, 85% and
75% of their incomes, respectively. If
their savings are in the ratio 8 : 9 : 20 and
the difference between the incomes of A
and C is Rs. 18,000 , then the income of
B is :
SSC CGL Tier II (13/09/2019)
(a) Rs. 24,000 (b) Rs. 27,000
(c) Rs. 30,000 (d) Rs. 36,000
Q.31. The ratio of income of A and B last
year was 4 : 3, respectively. The ratios of
their individual incomes of the last year
and the present year are 3 : 4 and 5 : 6,
respectively. If their total income for the
present year is Rs. 8.04 lakh, then the
income of B last year was :
SSC CGL Tier II (12/09/2019)
(a) Rs. 2.7 lakh (b) Rs. 3.6 lakh
(c) Rs. 2.4 lakh (d) Rs. 2.8 lakh
Q.32. The ratio of the income of A to that
of B is 5 : 7. A and B save Rs. 4000 and
Rs. 5000 respectively. If the expenditure
of A is equal to 66 % of the expenditure
2
3
of B, then the total income of A and B is :
SSC CGL Tier II (11/09/2019)
(a) Rs. 25,200 (b) Rs. 24,000
(c) Rs. 26,400 (d) Rs. 28,800
Q.33. The ratio between the divisor and
remainder is 3 : 2 and the ratio between
the divisor and the quotient is 7 : 12. If
the remainder is 14, then ?nd the
remainder when the dividend is divided
by 9.
SSC MTS 21/08/2019 (Morning)
(a) 3 (b) 6 (c) 4 (d) 5
Q.34. Ravi’s age is of Shyam’s age.
3
5
After x years the ratio of the ages of Ravi
and Shyam becomes 5 : 7. If initially the
sum of their ages is 32, then what is the
value of x ?
SSC MTS 08/08/2019 (Morning)
(a) 2 (b) 4 (c) 8 (d) 7
Q.35. What is the ratio between the
fourth proportional of 3, 4, 9 and the
mean proportional between 2 and 98?
SSC CHSL 11/07/2019 (Afternoon)
(a) 7 : 8 (b) 7 : 6 (c) 8 : 7 (d) 6 : 7
Q.36. Rs. 8000 is distributed among A, B
and C such that they receive notes of Rs.
500, Rs. 200 and Rs. 100 respectively.
The amounts received by them are in the
ratio 15 : 2 : 3. What was the ratio of the
numbers of notes of Rs. 500, Rs 200 and
Rs 100 ?
SSC CHSL 10/07/2019 (Morning)
(a) 3:1:3 (b) 3:3:1 (c) 4:1:2 (d) 3:2:2
Q.37. The ratio of incomes of A and B is
2 : 3 and that of their expenditure is 1 : 2.
If 90% of B’s expenditure is equal to the
income of A , then what is the ratio of the
savings of A and B?
SSC CHSL 02/07/2019 (Morning)
(a) 1 : 1 (b) 9 : 8 (c) 8 : 7 (d) 3 : 2
Q.38. A sum of Rs. 4360 was to be
divided among A , B , C and D in the ratio
of 3 : 4 : 5 : 8, but it was divided in the
ratio of : : : by mistake.
1
3
1
4
1
5
1
8
As a result:
SSC CHSL 01/07/2019 (Evening)
(a) A received Rs. 956 more
(b) B received Rs. 318 more
(c) D received Rs. 1144 less
(d) C received Rs. 132 less
Q.39. If a : b = 2 : 5 , c : b = 3 : 4 , then a :
b : c is equal to :
SSC CGL 12/06/2019 (Evening)
(a) 6 : 15 : 20 (b) 8 : 20 : 15
(c) 2 : 5 : 4 (d) 2 : 5 : 3
Q.40. A sum of Rs. x is divided among A ,
B and C such that the ratio of shares of A
and B is 7 : 12 and that of B and C is 8 : 5.
If the difference in the shares of A and C
is Rs. 214 , then the value of x is :
SSC CGL 07/06/2019 (Evening)
(a) 11556 (b) 11128 (c) 11770 (d) 11342
Q.41. The prices of two articles are in the
ratio 4 : 5. If the price of the ?rst article is
increased by x% and that of the other is
decreased by 30% , then the new prices
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Pinnacle Day: 49th - 52nd Ratio & Proportion
of A and B will be in the ratio 10 : 7. The
value of x is :
SSC CGL 07/06/2019 (Afternoon)
(a) 24.5 (b) 22.5 (c) 25 (d) 20
Q.42. The ratio of the ages of A and B,
four years ago, was 4 : 5. Eight years
from now, the ratio of the ages of A and
B will be 11 : 13. What is the sum of their
present ages?
SSC CGL 04/06/2019 (Morning)
(a) 80 years (b) 96 years
(c) 72 years (d) 76 years
Practice Questions
SSC CHSL 2023 Tier - 2
Q.43. A sum of money is divided among
A, B, and C in the ratio 4 : 3 : 6. If the
share of C is ?600 more than B, then how
much amount will A get more than B ?
SSC CHSL Tier II 02/11/2023
(a) ?200 ( b) ?150 (c) ?250 (d) ?100
Q.44. The ratio of the expenditure to the
savings of Richa is 2 : 1. If her income
and expenditure increase by 20% and
15%, respectively, then ?nd the
percentage increase in her savings.
SSC CHSL Tier II 10/01/2024
(a) 35% (b) 30% (c) 20% (d) 25%
Q.45. The ratio of prices of Coffee and
Tea is 3 : 4 and the ratio of their
quantities consumed by a family is 4 : 7.
Find the ratio of expenditures on Coffee
and Tea.
SSC CHSL Tier II 10/01/2024
(a) 3 : 7 (b) 7 : 3 (c) 7 : 4 (d) 4 : 7
Q.46. ?7,786 is divided among A, B and C
in such a manner that the ratio of the
amount of A to that of B is 3 : 4 and the
ratio of the amount of B to that of C is 12
: 13. The amount of money received by B
is:
SSC CHSL Tier II 10/01/2024
(a) ?7,138 (b) ?2,977
(c) ?2,748 (d) ?5,038
SSC CPO 2023 Tier - 1
Q.47. The areas of the two triangles are
in the ratio 4 : 3 and their heights are in
the ratio 6 : 5. Find the ratio of their
bases.
SSC CPO 03/10/2023 (1st Shift)
(a) 5 : 6 (b) 10 : 9 (c) 9 : 10 (d) 6 : 5
Q.48. If = , then the value of
??
4 ??
3
4
is
2 ?? + 3 ??
?? - 2 ??
SSC CPO 05/10/2023 (2nd Shift)
(a) 8 (b) 6 (c) 9 (d) 7
SSC MTS 2023 Tier - 1
Q.49. P and Q are inversely proportional
to each other and P is 10, when Q is 6.
What will be the value of Q when P is 15?
SSC MTS 01/09/2023 (2nd Shift)
(a) 9 (b) 4 (c) 10 (d) 5
Q.50. The mean proportion of (3 + )
2
2 2
and (3 - 2 )
2
is: 2
SSC MTS 04/09/2023 (1st Shift)
(a) 3 + 2 (b) 5 (c) 2 (d) 1 2 2
Q.51. Two numbers are in the ratio of 6 :
7. If the difference between these
numbers is 16, then ?nd the numbers.
SSC MTS 04/09/2023 (2nd Shift)
(a) 96, 112 (b) 80, 96
(c) 120, 136 (d) 104, 120
Q.52. Pro?t of ?29,120 is divided among
A, B and C so that A's share is 2 times
1
2
B's and B's share is 1 times C. Find B's
1
5
share.
SSC MTS 05/09/2023 (2nd Shift)
(a) ?6,940 (b) ?7,820 (c) ?6,720 (d) ?7,140
Q.53. The mean proportion of and ??
??
??
2
is ______ .
SSC MTS 05/09/2023 (2nd Shift)
(a) ab (b) (c) (d)
??
??
??
??
??
2 ??
Q.54. Rupees 66,000 is to be divided
amongst Asha, Bhupinder and Gargi in
such a way that ratio of their shares is to
be: Asha : Bhupinder = 9 : 5 and
Bhupinder : Gargi = 2 : 1 . How much
should Asha get ?
SSC MTS 05/09/2023 (3rd Shift)
(a) ?38,000 (b) ?36,000
(c) ?32,000 (d) ?34,000
Q.55. A certain sum is to be divided
between A, B, and C in the ratio 2 : 5 : 7.
But by mistake, it was divided in the ratio
5 : 2 : 7. Thus B loses by ?150. Find the
sum.
SSC MTS 06/09/2023 (1st Shift)
(a) ?700 (b) ?850 (c) ?900 (d) ?625
Q.56. If p : q = 5 : 2, then p² - q² : p² + q² = ?
SSC MTS 06/09/2023 (2nd Shift)
(a) 29 : 21 (b) 4 : 3 (c) 3 : 4 (d) 21 : 29
Q.57. If A : B = : , B : C = :
1
3
1
5
1
7
1
8
and C : D = : , then A : B : C : D is:
1
10
1
21
SSC MTS 06/09/2023 (3rd Shift)
(a) 40 : 24 : 21 : 10 (b) 48 : 23 : 25 : 8
(c) 8 : 3 : 7 : 5 (d) 14 : 24 : 28 : 10
Q.58. The marks scored by a student are
directly proportional to the time invested
in studies. If the student gets 60 marks
when he studies 4 hours a day, then how
many hours he should use in his studies
daily to get 75 marks ?
SSC MTS 08/09/2023 (1st Shift)
(a) 4.5 (b) 5 (c) 5.5 (d) 6
Q.59. Three numbers are in the ratio 5 : 2
: 7. The sum of their squares is 3822. The
biggest number is :
SSC MTS 08/09/2023 (2nd Shift)
(a) 35 (b) 38 (c) 78 (d) 49
Q.60. Among four numbers the sum of
the smallest and largest is 72 more than
the sum of middle two numbers. If the
numbers are in the ratio 6 : 7 : 15 : 19,
then the smallest number is :
SSC MTS 08/09/2023 (2nd Shift)
(a) 72 (b) 144 (c) 168 (d) 216
Q.61. If the income of T is 8 times his
savings, then his expenditure is ___ times
his savings.
SSC MTS 11/09/2023 (3rd Shift)
(a) 6 (b) 7 (c) 8 (d) 5
Q.62. The ratio of number of students in
schools A and B is 5 : 8. If the number of
students in schools A and B is increased
by 20% and 15%, respectively, ?nd the
new ratio of students in schools A and B,
respectively.
SSC MTS 12/09/2023 (2nd Shift)
(a) 15 : 23 (b) 15 : 13
(c) 13 : 15 (d) 12 : 13
Q.63. The ratio of the number of boys to
the number of girls in a school of 1650
students is 6 : 5. If 124 new boys are
admitted and few new girls are admitted,
the ratio changes to 4 : 3. What is the
ratio of the newly admitted girls to the
newly admitted boys ?
SSC MTS 13/09/2023 (1st Shift)
(a) 3 : 4 (b) 62 : 9 (c) 4 : 3 (d) 9 : 62
Q.64. In a class of boys and girls, the
number of girls is twice the number of
boys. If 20 more boys join the class, the
ratio of girls and boys is 1: 1. How many
total students were there in the class
initially?
SSC MTS 14/09/2023 (1st Shift)
(a) 60 (b) 75 (c) 45 (d) 90
Q.65. If A : B : C = 3 : 4 : 5, then ??
2
+ ??
2
: is: ??
2
- ??
2
SSC MTS 14/09/2023 (3rd Shift)
(a) 3 : 2 (b) 4 : 5 (c) 5 : 3 (d) 3 : 5
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Page 5
Pinnacle Day: 49th - 52nd Ratio & Proportion
Ratio & Proportion
Key - points:-
1) What are antecedent and consequent?
In the form ; x is called the ?? : ??
antecedent and y is called consequent .
2) can also be written as ?? : ??
??
??
3) Duplicate ratio (square) :-
Duplicate ratio of x : y will be ??
2
: ??
2
4) Sub-duplicate Ratio (square root):-
Sub-duplicate Ratio of x : y will be ?? : ??
5) Triplicate Ratio (cube) :-
Triplicate ratio of x : y will be ??
3
: ??
3
6) Sub-triplicate Ratio (cube root)
Sub-triplicate Ratio of x : y will be
3
?? :
3
??
7) Inverse ratio :- x : y will be y : x
8) Compound Ratio : If two or more
ratios are given, then the antecedent of
one is multiplied with antecedent of the
other and respective consequents are
also multiplied.
If a : b, c : d and e : f are three ratios, then
their compound ratio will be .
??????
??????
9) 3
rd
Proportional:- 3
rd
proportion of a
and b i.e. a : b :: b : x ?
Then , x =
??
2
??
10) 4
th
Proportional: 4
th
proportional of a,
b and c i.e. a : b :: c : x
Then , x =
?? × ??
??
11) Componendo and dividendo rule:
If a : b :: c : d , Then ?
?? + ??
?? - ??
=
?? + ??
?? - ??
12) Mean Proportion : Mean proportion
of two numbers, a and b, is given by . ????
Partnership
Concept 1
The ratio of pro?ts of two or more
partners will be equal to the ratio of their
respective equivalent investment ratio.
Equivalent investment = (Amount
Invested) (Time for which the amount ×
is invested).
We will take some examples to
understand the concepts of partnership.
Example 1: A invests Rs. 10,000 and B
invests Rs. 20,000 for a period of 1 year
each. The pro?t, after 1 year will be
divided in the ratio:
= =
???????????? ???? ??
???????????? ???? ??
10000 × 12
20000 × 12
1
2
Example 2: A invests Rs.100 in a
business. After 6 months B joins with an
investment of Rs. 200. At the end of 1
year C joins with an investment of
Rs.100. What will be the ratio of pro?t
after 3 years?
Example 3: In the previous case if the
total pro?t after 3 years is 10,000. What
will be the share of A?
Share of A in total pro?t =
10,000 =
3
3 + 5 + 2
×
3
10
× 10000
? 3 × 1000 = 3000
Note: In case someone invests
in-between the total period of time, just
take care for what time an amount is
invested. Similarly there can be a case
when someone opts out in that case
also, the time for which the amount was
invested will be taken into consideration
and not the full period.
Concept 2
If = = = = K, where K is
??
??
??
??
??
??
??
??
constant . Then , K =
?? + ?? + ?? + ??
?? + ?? + ?? + ??
Example : = = K, Find the
1 + ??
2 - ??
9 - ??
3 + ??
value of K ?
Sol . :- K = = = 2
1 + ?? + 9 - ??
2 - ?? + 3 + ??
10
5
Concept 3
If two or three ratios are given , and we
have to ?nd an individual ratio of all of
them, then we take LCM of the common
entities and then balancing the common
entities ,we get the required ratio.
Example :- a : b = 3 : 4 , b : c = 6 : 7.
LCM of the common entities i.e b = (4, 6)
= 12
a : b = 3 : 4 ) × 3 = 9 : 12
b : c = 6 : 7 ) × 2 = 12 : 14
So, a : b : c = 9 : 12 : 14
Note : In case there are more than three
ratios given , then the LCM approach will
be tedious in ?nding the individual ratio
of the given entities.
Alternative method
If a : b = 2 : 3, b : c = 4 : 5
c : d = 6 : 7, d : e = 1 : 2
To understand this concept we will take
some examples
Example 1 : ?5600 is to be divided
among A, B, C & D in such a way that the
ratio of share of A : B is 1 : 2, B : C is 3 : 1
, C : D is 2 : 3, ?nd the share of A and B
taken together ?
Share of A : B = 1 : 2
Share of B : C = 3 : 1
Share of C : D = 2 : 3
A : B : C : D ?
1 × 3 × 2 : 2 × 3 × 2 : 2 × 1 × 2 : 2 × 1 × 3
= 6 : 12 : 4 : 6 or 3 : 6 : 2 : 3
Sum of the share of all of them = 3 + 6 +
2 + 3 = 14 unit
Total share of (A + B) = × 5600
6 + 3
14
= 9 × 400 = ?3600
Example 2 : Sum of ? x is divided among
A, B, C such that the ratio of the shares of
A and B is 6 : 7 and that of B and C is 3 :
2. If the difference of the share of A and
C is ?540 . Find the value of x
Share of A and B = 6 : 7
Share of B and C = 3 : 2
Ratio of the shares of A, B and C = 6 × 3 :
3 × 7 : 7 × 2 = 18 : 21: 14
Diff. of A and C = 18 - 14 = 4 unit, which
corresponds to ?540
Total share of A, B and C = 18 + 21 + 14
= 53 unit = × 53 = ? 7155
540
4
Concept 4
If numerator and denominator of a ratio
is multiplied and divided by same
number, the ratio remains unchanged .
E.g. :- = =
??
??
?? × ??
?? × ??
??
??
??
??
Ratio is independent of change in scale
only and not of origin.
Concept 5
If there is ‘n’ number of unequal fractions
such as , , , then
?? 1
?? 1
?? 2
?? 2
?? 3
?? 3
?? 4
?? 4
.....
????
????
the ratio of (a
1
+a
2
+a
3
+..a
n
) and (b
1
+ b
2
+
b
3
+ … b
n
) lies between lowest and
highest values of these fractions.
Example:- three unequal fractions are
1
2
, , . So, the ratio of (1 + 2 + 4) : (2 + 3
2
3
4
7
+ 7) = 7:12. Among these fractions,
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Pinnacle Day: 49th - 52nd Ratio & Proportion
lowest fraction is and the highest
1
2
fraction is so, the required value lies
2
3
between and .
1
2
2
3
Concept 6:
If aA = bB = cC, where a,b,c are constants
and A, B, C are variables. Then the ratio
of A : B : C = b × c : c × a : a × b.
Example: if 3A = 4B = 5C, then ?nd A:B:C
The ratio of A : B : C = 4 × 5 : 5 × 3 : 3 × 4
= 20 : 15 : 12
Variety Questions
Q.1. The concentration of three wines A,
B and C are 10%, 20% and 30%,
respectively. They are mixed in the ratio 2
: 3 : x resulting in a 23% concentration
solution. Find the value of x.
SSC CHSL Tier II 02/11/2023
(a) 7 (b) 6 (c) 8 (d) 5
Q.2. In a school of 720 students, the ratio
of boys to girls is 3 : 5. Find how many
new boys may be allowed to the school if
18 new girls are admitted, so that the
ratio of boys to girls changes to 2 : 3.
SSC CPO 05/10/2023 (3rd Shift)
(a) 42 (b) 50 (c) 44 (d) 38
Q.3. Ram has 12 hens and 5 cows,
Shyam has 18 hens and 9 cows,
Preetham has 4 hens and 8 cows, and
Vinay has 10 hens and 7 cows. Who has
a greater ratio of hens to cows?
SSC CPO 05/10/2023 (2nd Shift)
(a) Shyam (b) Preetham
(c) Vinay (d) Ram
Q.4. A company is manufacturing boxes
of three types - plastic, wood and glass.
The ratio of the numbers of plastic, wood
and glass boxes is 2 : 3 : 5. The
difference between the numbers of wood
and glass boxes is 144. If the number of
plastic boxes is increased by 25%, then
what will be the number of plastic boxes
now ?
SSC CPO 04/10/2023 (1st Shift)
(a) 144 (b) 216 (c) 360 (d) 180
Q.5. Find the fourth proportional of 12
35
,3
12
and 4
12
.
SSC MTS 14/09/2023 (3rd Shift)
(a) 12
-23
(b) 3
24
(c) 12
-11
(d) 4
24
Q.6. Three numbers are in the ratio 1 : 2 :
3. By adding 5 to each of the numbers
then the ratio changes to 2 : 3 : 4. The
smallest number is:
SSC MTS 14/09/2023 (1st Shift)
(a) 5 (b) 15 (c) 12 (d) 20
Q.7. When x = 1 then y is directly
proportional to x + 3 and y = 8. When z =
6 then x is inversely proportional to z and
x = 2. Find the relation between y and z.
SSC MTS 12/09/2023 (2nd Shift)
(a) (y - 6) / z = 24 (b) (y - 6) / z = 12
(c) z(y - 6) = 12 (d) z(y - 6) = 24
Q.8. The average of the two numbers is
48. If 3 is added to a smaller number,
then the ratio between them is 11 : 20.
Find the larger number. (Round up to two
decimal places).
SSC MTS 05/09/2023 (3rd Shift)
(a) 40.87 (b) 3.87 (c) 63.87 (d) 70.87
Q.9. Arrange the ratios in ascending
order 5 : 3 , 6 : 3 and 3.5 : 4.5.
1
3
1
4
1
8
SSC MTS 05/09/2023 (1st Shift)
(a) 3.5 : 4.5 < 5 : 3 < 6 : 3
1
3
1
4
1
8
(b) 6 : 3 < 5 : 3 < 3.5 : 4.5
1
4
1
8
1
3
(c) 5 : 3 < 3.5 : 4.5 < 6 : 3
1
3
1
4
1
8
(d) 5 : 3 < 6 : 3 < 3.5 : 4.5
1
3
1
4
1
8
Q.10. The incomes of P , Q and R are in
the ratio of 9 : 15 : 10 and their savings
are in the ratio is 10 : 15 : 12. If R spends
60% of his income, what is the ratio of
the expenditures of P , Q and R?
SSC MTS 05/09/2023 (1st Shift)
(a) 18 : 17 : 30 (b) 17 : 30 : 18
(c) 17 : 18 : 30 (d) 18 : 30 : 17
Q.11. Find the fourth proportional to
( ?? + ?? )
2
× ( ??
3
- ??
3
), ( ??
3
+ ??
3
), ( ??
2
- ??
2
).
SSC MTS 01/09/2023 (2nd Shift)
(a) (b)
( ??
2
- ???? + ??
2
)
( ?? + ?? )
( ??
2
+ ???? + ??
2
)
( ?? - ?? )
(c) (d)
( ??
2
- ???? + ??
2
)
( ??
2
+ ???? + ??
2
)
( ??
2
+ ???? + ??
2
)
( ??
2
- ??
2
)
Q.12. Two numbers A and B are such
that the sum of 6% of A and 4% of B is
2
5
of the sum of 7% of A and 11% of B, then
the ratio A : B is:
SSC MTS 01/09/2023 (1st Shift)
(a) 3 : 7 (b) 5 : 8 (c) 1 : 8 (d) 1 : 7
Q.13. A certain sum was to be divided
between A and B in the ratio 8 : 5.
However, by mistake, it was divided in the
ratio 5 : 8. Thus, A gets 300 less than ?
his original share. Find the sum.
SSC CHSL 17/08/2023 (4th Shift)
(a) ?2,600 (b) ?1,500 (c) ?1,300 (d) ?600
Q.14. When P is subtracted from each of
the numbers 8, 6, 2 and 9, the numbers so
obtained in this order are in proportion.
What is the mean proportional between
(3P - 6) and (9P - 4) ?
SSC CHSL 10/08/2023 (4th Shift)
(a) 26 (b) 28 (c) 29 (d) 24
Q.15. A man invests ?44,000 in some
shares in the ratio 1 : 4 : 5 which pay
dividends of 10%, 15% and 25% on his
investment for one year, respectively. His
total dividend income is:
SSC CHSL 07/08/2023 (1st Shift)
(a) ? 7,850 (b) ? 8,580
(c) ? 7,970 (d) ? 8,510
Q.16. A sum of money is divided among A,
B, C in the ratio 3 : 2 : 5, respectively. If the
share of C is ?300 more than B. then how
much more money will A get than B ?
SSC CHSL 03/08/2023 (1st Shift)
(a) ?150 (b) ?75 (c) ?100 (d) ?125
Q.17. The mean proportional of (a + b)
, (a - b) is: ( ?? - ?? )
3
( ?? + ?? )
3
SSC CGL 25/07/2023 (4th shift)
(a) (b) (a b) ( ?? + ?? )
2
( ?? - ?? )
2
( ?? + ?? )
2
-
(c) (a + b) (d) ( ?? - ?? )
2
??
2
- ??
2
Q.18. The seats for Mathematics, English
and Chemistry in a school are in the ratio
of 6 : 4 : 7. If these seats are increased
by 20%, 40% and 60%, respectively, the
ratio of the increased seats is:
SSC CGL 19/07/2023 (2nd shift)
(a) 9 : 7 : 8 (b) 9 : 7 : 14
(c) 1 : 2 : 3 (d) 7 : 9 : 14
Q.19. In a party hall, there are people in
blue and red dresses. The ratio of the
number of men in blue to the number of
women in red is 3 : 7. The ratio of men in
red to the number of women in blue is 2 :
1. If the ratio of the number of people in
blue to the number of people in red is 35 :
76, then what is the ratio of the number
of men to the number of women ?
SSC MTS 04/05/2023 (Morning)
(a) 47 : 51 (b) 40 : 43
(c) 62 : 57 (d) 52 : 59
Q.20. P's income is 250 percent of Q's
income and P's expenditure is 180
percent of Q's expenditure. If P's income
is 400 percent of Q's expenditure, then
what is the respective ratio of P's savings
and Q's savings?
SSC CHSL 17/03/2023 (3rd Shift)
(a) 8 : 3 (b) 11 : 3 (c) 11 : 5 (d) 5 : 2
Q.21. The number of units manufactured
by company A was 12500 units in 2019
and 10625 units in 2020. While in
company B, the production fell from
34000 units in 2019 to 30600 units in
2020. If X and Y are the percentage
decrease in the number of units
manufactured by company A and B
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Pinnacle Day: 49th - 52nd Ratio & Proportion
respectively from 2019 to 2020, then
what will be the ratio of X and Y?
SSC CGL 13/12/2022 (1st Shift)
(a) 5 : 3 (b) 3 : 4 (c) 3 : 2 (d) 8 : 5
Q.22. Find the mean proportion of
and .
??
3
+ ??
3
?? - ??
??
2
- ??
2
??
2
- ???? + ??
2
SSC CGL 06/12/2022 (3rd Shift)
(a) 1 (b) a + b (c) (d)
?? + ??
?? - ??
?? + ??
Q.23. In an o?ce with 40 o?cers, the
average salaries of class-A, class-B and
class-C o?cers are ?600, ?750 and
?1,000 a day, respectively. The number of
class-A, class-B and class-C o?cers in
the o?ce are in the ratio 5 : 4 : 1,
respectively. Find the monthly average
salary (in ?) of an o?cers, all the 40 of
them taken together. [Assume the
number of days in a month to be 30.]
SSC MTS 08/07/2022 (Morning)
(a) 25,800 (b) 21,000
(c) 24,030 (d) 24,600
Q.24. The ratio of income of A to that of
B is 4 : 3. The expenditure of A is of
5
12
his income and the expenditure of B is
of his income. The difference
7
15
between their expenditure is ?4,500. Find
the income of B.
SSC CHSL 25/05/2022 (Evening)
(a) ?49,625 (b) ?48,625
(c) ?51,625 (d) ?50,625
Q.25. A sum of ?46,800 is divided among
A, B, C and D in such a way that the ratio
of the combined share of A and D to the
combined share of B and C is 8 : 5. The
ratio of the share of B to that of C is 5: 4.
A receives ?18,400. If x is the difference
between the shares of A and B and y is
the difference between the shares of C
and D, then what is the value of (x - y) (in
?) ?
SSC CGL Tier II (29/01/2022)
(a) 6000 (b) 6500 (c) 5000 (d) 7000
Q.26. If a number of pens and pencils are
bought in the ratio of 5 : 3, then Ashok
has to pay ?44. If the ratio is changed as
3 : 5, then he has to pay ?36. Find the
ratio of the price of one pen to one
pencil.
SSC MTS 11/10/2021 (Evening)
(a) 5 : 3 (b) 7 : 3 (c) 8 : 5 (d) 7 : 4
Q.27. Atul purchased Bread costing
Rs.20 and gave a 100 rupee note to the
shopkeeper. The shopkeeper gave the
balance money in coins of denomination
2, 5, and 10. If these coins are in the ratio
5 : 4 : 1, then how many 5 coins did the
shopkeeper give?
SSC CGL 03/08/2021 (Evening)
(a) 5 (b) 6 (c) 8 (d) 4
Q.28. In a school, of the number of
3
8
students are girls and the rest are boys,
One - third of the number of boys are
below 10 years and of the number of
2
3
girls is also below 10 years. If the
number of students of age 10 or more
years is 260, then the number of boys in
the school is:
SSC CGL Tier II (15/11/2020)
(a) 280 (b) 300 (c) 234 (d) 312
Q.29. By adding 3 and 5 in numerator
and denominator of a fraction it
becomes . If 1 and 3 are subtracted
2
3
and added from numerator and
denominator respectively, it becomes .
2
5
Find the fraction.
SSC CHSL 19/10/2020 (Morning shift)
(a) (b) (c) (d)
5
7
6
7
7
6
7
5
Q.30. A, B and C spend 80%, 85% and
75% of their incomes, respectively. If
their savings are in the ratio 8 : 9 : 20 and
the difference between the incomes of A
and C is Rs. 18,000 , then the income of
B is :
SSC CGL Tier II (13/09/2019)
(a) Rs. 24,000 (b) Rs. 27,000
(c) Rs. 30,000 (d) Rs. 36,000
Q.31. The ratio of income of A and B last
year was 4 : 3, respectively. The ratios of
their individual incomes of the last year
and the present year are 3 : 4 and 5 : 6,
respectively. If their total income for the
present year is Rs. 8.04 lakh, then the
income of B last year was :
SSC CGL Tier II (12/09/2019)
(a) Rs. 2.7 lakh (b) Rs. 3.6 lakh
(c) Rs. 2.4 lakh (d) Rs. 2.8 lakh
Q.32. The ratio of the income of A to that
of B is 5 : 7. A and B save Rs. 4000 and
Rs. 5000 respectively. If the expenditure
of A is equal to 66 % of the expenditure
2
3
of B, then the total income of A and B is :
SSC CGL Tier II (11/09/2019)
(a) Rs. 25,200 (b) Rs. 24,000
(c) Rs. 26,400 (d) Rs. 28,800
Q.33. The ratio between the divisor and
remainder is 3 : 2 and the ratio between
the divisor and the quotient is 7 : 12. If
the remainder is 14, then ?nd the
remainder when the dividend is divided
by 9.
SSC MTS 21/08/2019 (Morning)
(a) 3 (b) 6 (c) 4 (d) 5
Q.34. Ravi’s age is of Shyam’s age.
3
5
After x years the ratio of the ages of Ravi
and Shyam becomes 5 : 7. If initially the
sum of their ages is 32, then what is the
value of x ?
SSC MTS 08/08/2019 (Morning)
(a) 2 (b) 4 (c) 8 (d) 7
Q.35. What is the ratio between the
fourth proportional of 3, 4, 9 and the
mean proportional between 2 and 98?
SSC CHSL 11/07/2019 (Afternoon)
(a) 7 : 8 (b) 7 : 6 (c) 8 : 7 (d) 6 : 7
Q.36. Rs. 8000 is distributed among A, B
and C such that they receive notes of Rs.
500, Rs. 200 and Rs. 100 respectively.
The amounts received by them are in the
ratio 15 : 2 : 3. What was the ratio of the
numbers of notes of Rs. 500, Rs 200 and
Rs 100 ?
SSC CHSL 10/07/2019 (Morning)
(a) 3:1:3 (b) 3:3:1 (c) 4:1:2 (d) 3:2:2
Q.37. The ratio of incomes of A and B is
2 : 3 and that of their expenditure is 1 : 2.
If 90% of B’s expenditure is equal to the
income of A , then what is the ratio of the
savings of A and B?
SSC CHSL 02/07/2019 (Morning)
(a) 1 : 1 (b) 9 : 8 (c) 8 : 7 (d) 3 : 2
Q.38. A sum of Rs. 4360 was to be
divided among A , B , C and D in the ratio
of 3 : 4 : 5 : 8, but it was divided in the
ratio of : : : by mistake.
1
3
1
4
1
5
1
8
As a result:
SSC CHSL 01/07/2019 (Evening)
(a) A received Rs. 956 more
(b) B received Rs. 318 more
(c) D received Rs. 1144 less
(d) C received Rs. 132 less
Q.39. If a : b = 2 : 5 , c : b = 3 : 4 , then a :
b : c is equal to :
SSC CGL 12/06/2019 (Evening)
(a) 6 : 15 : 20 (b) 8 : 20 : 15
(c) 2 : 5 : 4 (d) 2 : 5 : 3
Q.40. A sum of Rs. x is divided among A ,
B and C such that the ratio of shares of A
and B is 7 : 12 and that of B and C is 8 : 5.
If the difference in the shares of A and C
is Rs. 214 , then the value of x is :
SSC CGL 07/06/2019 (Evening)
(a) 11556 (b) 11128 (c) 11770 (d) 11342
Q.41. The prices of two articles are in the
ratio 4 : 5. If the price of the ?rst article is
increased by x% and that of the other is
decreased by 30% , then the new prices
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Pinnacle Day: 49th - 52nd Ratio & Proportion
of A and B will be in the ratio 10 : 7. The
value of x is :
SSC CGL 07/06/2019 (Afternoon)
(a) 24.5 (b) 22.5 (c) 25 (d) 20
Q.42. The ratio of the ages of A and B,
four years ago, was 4 : 5. Eight years
from now, the ratio of the ages of A and
B will be 11 : 13. What is the sum of their
present ages?
SSC CGL 04/06/2019 (Morning)
(a) 80 years (b) 96 years
(c) 72 years (d) 76 years
Practice Questions
SSC CHSL 2023 Tier - 2
Q.43. A sum of money is divided among
A, B, and C in the ratio 4 : 3 : 6. If the
share of C is ?600 more than B, then how
much amount will A get more than B ?
SSC CHSL Tier II 02/11/2023
(a) ?200 ( b) ?150 (c) ?250 (d) ?100
Q.44. The ratio of the expenditure to the
savings of Richa is 2 : 1. If her income
and expenditure increase by 20% and
15%, respectively, then ?nd the
percentage increase in her savings.
SSC CHSL Tier II 10/01/2024
(a) 35% (b) 30% (c) 20% (d) 25%
Q.45. The ratio of prices of Coffee and
Tea is 3 : 4 and the ratio of their
quantities consumed by a family is 4 : 7.
Find the ratio of expenditures on Coffee
and Tea.
SSC CHSL Tier II 10/01/2024
(a) 3 : 7 (b) 7 : 3 (c) 7 : 4 (d) 4 : 7
Q.46. ?7,786 is divided among A, B and C
in such a manner that the ratio of the
amount of A to that of B is 3 : 4 and the
ratio of the amount of B to that of C is 12
: 13. The amount of money received by B
is:
SSC CHSL Tier II 10/01/2024
(a) ?7,138 (b) ?2,977
(c) ?2,748 (d) ?5,038
SSC CPO 2023 Tier - 1
Q.47. The areas of the two triangles are
in the ratio 4 : 3 and their heights are in
the ratio 6 : 5. Find the ratio of their
bases.
SSC CPO 03/10/2023 (1st Shift)
(a) 5 : 6 (b) 10 : 9 (c) 9 : 10 (d) 6 : 5
Q.48. If = , then the value of
??
4 ??
3
4
is
2 ?? + 3 ??
?? - 2 ??
SSC CPO 05/10/2023 (2nd Shift)
(a) 8 (b) 6 (c) 9 (d) 7
SSC MTS 2023 Tier - 1
Q.49. P and Q are inversely proportional
to each other and P is 10, when Q is 6.
What will be the value of Q when P is 15?
SSC MTS 01/09/2023 (2nd Shift)
(a) 9 (b) 4 (c) 10 (d) 5
Q.50. The mean proportion of (3 + )
2
2 2
and (3 - 2 )
2
is: 2
SSC MTS 04/09/2023 (1st Shift)
(a) 3 + 2 (b) 5 (c) 2 (d) 1 2 2
Q.51. Two numbers are in the ratio of 6 :
7. If the difference between these
numbers is 16, then ?nd the numbers.
SSC MTS 04/09/2023 (2nd Shift)
(a) 96, 112 (b) 80, 96
(c) 120, 136 (d) 104, 120
Q.52. Pro?t of ?29,120 is divided among
A, B and C so that A's share is 2 times
1
2
B's and B's share is 1 times C. Find B's
1
5
share.
SSC MTS 05/09/2023 (2nd Shift)
(a) ?6,940 (b) ?7,820 (c) ?6,720 (d) ?7,140
Q.53. The mean proportion of and ??
??
??
2
is ______ .
SSC MTS 05/09/2023 (2nd Shift)
(a) ab (b) (c) (d)
??
??
??
??
??
2 ??
Q.54. Rupees 66,000 is to be divided
amongst Asha, Bhupinder and Gargi in
such a way that ratio of their shares is to
be: Asha : Bhupinder = 9 : 5 and
Bhupinder : Gargi = 2 : 1 . How much
should Asha get ?
SSC MTS 05/09/2023 (3rd Shift)
(a) ?38,000 (b) ?36,000
(c) ?32,000 (d) ?34,000
Q.55. A certain sum is to be divided
between A, B, and C in the ratio 2 : 5 : 7.
But by mistake, it was divided in the ratio
5 : 2 : 7. Thus B loses by ?150. Find the
sum.
SSC MTS 06/09/2023 (1st Shift)
(a) ?700 (b) ?850 (c) ?900 (d) ?625
Q.56. If p : q = 5 : 2, then p² - q² : p² + q² = ?
SSC MTS 06/09/2023 (2nd Shift)
(a) 29 : 21 (b) 4 : 3 (c) 3 : 4 (d) 21 : 29
Q.57. If A : B = : , B : C = :
1
3
1
5
1
7
1
8
and C : D = : , then A : B : C : D is:
1
10
1
21
SSC MTS 06/09/2023 (3rd Shift)
(a) 40 : 24 : 21 : 10 (b) 48 : 23 : 25 : 8
(c) 8 : 3 : 7 : 5 (d) 14 : 24 : 28 : 10
Q.58. The marks scored by a student are
directly proportional to the time invested
in studies. If the student gets 60 marks
when he studies 4 hours a day, then how
many hours he should use in his studies
daily to get 75 marks ?
SSC MTS 08/09/2023 (1st Shift)
(a) 4.5 (b) 5 (c) 5.5 (d) 6
Q.59. Three numbers are in the ratio 5 : 2
: 7. The sum of their squares is 3822. The
biggest number is :
SSC MTS 08/09/2023 (2nd Shift)
(a) 35 (b) 38 (c) 78 (d) 49
Q.60. Among four numbers the sum of
the smallest and largest is 72 more than
the sum of middle two numbers. If the
numbers are in the ratio 6 : 7 : 15 : 19,
then the smallest number is :
SSC MTS 08/09/2023 (2nd Shift)
(a) 72 (b) 144 (c) 168 (d) 216
Q.61. If the income of T is 8 times his
savings, then his expenditure is ___ times
his savings.
SSC MTS 11/09/2023 (3rd Shift)
(a) 6 (b) 7 (c) 8 (d) 5
Q.62. The ratio of number of students in
schools A and B is 5 : 8. If the number of
students in schools A and B is increased
by 20% and 15%, respectively, ?nd the
new ratio of students in schools A and B,
respectively.
SSC MTS 12/09/2023 (2nd Shift)
(a) 15 : 23 (b) 15 : 13
(c) 13 : 15 (d) 12 : 13
Q.63. The ratio of the number of boys to
the number of girls in a school of 1650
students is 6 : 5. If 124 new boys are
admitted and few new girls are admitted,
the ratio changes to 4 : 3. What is the
ratio of the newly admitted girls to the
newly admitted boys ?
SSC MTS 13/09/2023 (1st Shift)
(a) 3 : 4 (b) 62 : 9 (c) 4 : 3 (d) 9 : 62
Q.64. In a class of boys and girls, the
number of girls is twice the number of
boys. If 20 more boys join the class, the
ratio of girls and boys is 1: 1. How many
total students were there in the class
initially?
SSC MTS 14/09/2023 (1st Shift)
(a) 60 (b) 75 (c) 45 (d) 90
Q.65. If A : B : C = 3 : 4 : 5, then ??
2
+ ??
2
: is: ??
2
- ??
2
SSC MTS 14/09/2023 (3rd Shift)
(a) 3 : 2 (b) 4 : 5 (c) 5 : 3 (d) 3 : 5
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Pinnacle Day: 49th - 52nd Ratio & Proportion
SSC CHSL 2023 Tier - 1
Q.66. Find the third proportional of 25
and 45.
SSC CHSL 02/08/2023 (1st Shift)
(a) 85 (b) 65 (c) 81 (d) 76
Q.67. Find the fourth proportion to 0.24,
0.6 and 20.
SSC CHSL 03/08/2023 (2nd Shift)
(a) 50 (b) 24 (c) 54 (d) 48
Q.68. The cost of 3 cups and 5 plates is
?1,080 and the cost of 2 cups and 4
plates is ?840. Find the ratio of the cost
of a cup to the cost of a plate.
SSC CHSL 03/08/2023 (3rd Shift)
(a) 1 : 3 (b) 2 : 3 (c) 1 : 1 (d) 1 : 2
Q.69. The compound ratio of 3: 4 and 6:
7 is 36: x. Find x.
SSC CHSL 03/08/2023 (4th Shift)
(a) 64 (b) 75 (c) 56 (d) 48
Q.70. Find 2 numbers such that their
mean proportional is 25 and their third
proportional is 25.
SSC CHSL 07/08/2023 (1st Shift)
(a) 5 and 5 (b) 5 and 25
(c) 25 and 125 (d) 25 and 25
Q.71. The present age of a father is twice
that of his son. 8.5 years hence the ratio
would be 7 : 4. Find the son's present
age.
SSC CHSL 07/08/2023 (2nd Shift)
(a) 25.5 years (b)16.5 years
(c) 20.5 years (d) 24.6 years
Q.72. The sum of the amount that
Sunaina and Ranjan have is ?23 and the
difference of their amount is ?7. The ratio
of the amount that Sunaina and Ranjan
have is:
SSC CHSL 07/08/2023 (3rd Shift)
(a) 5 : 3 (b) 7 : 15 (c)15: 8 (d) 2 : 17
Q.73. Two numbers are in the ratio of 1:
2. If 7 is added to both, their ratio
changes to 3 : 5. The greater number is:
SSC CHSL 07/08/2023 (3rd Shift)
(a) 30 (b) 18 (c) 14 (d) 28
Q.74. The difference between 24 and the
mean proportional of 7 and 63 is:
SSC CHSL 07/08/2023 (4th Shift)
(a) 3 (b) 2 (c) 5 (d) 4
Q.75. What is the mean proportional
between 3 and 27 ?
SSC CHSL 08/08/2023 (1st Shift)
(a) 30 (b) 81 (c) 15 (d) 9
Q.76. If a : b = 5 : 7, then
will be : 6 ??
2
- 2 ??
2
( )
: ( ??
2
- ??
2
)
SSC CHSL 08/08/2023 (4th Shift)
(a) 12 : 5 (b) 21 : 5 (c) 13 : 6 (d) 17 : 8
Q.77. Find the fourth proportion of the
numbers
rd
of 15,
th
of 25,
th
of
1
3
4
5
3
7
35:
SSC CHSL 09/08/2023 (1st Shift)
(a) 65 (b) 55 (c) 60 (d) 50
Q.78. The ratio of Ram's salary to
Shyam's salary is 3 : 4. The ratio of
Shyam's salary to Ghanshyam's salary is
5 : 6. What will be the ratio of Ram's
salary to Ghanshyam's salary ?
SSC CHSL 09/08/2023 (3rd Shift)
(a) 3 : 5 (b) 5 : 8 (c) 4 : 5 (d) 3 : 8
Q.79. What is the fourth proportional of
3 , 5 and 3 ? 5 8 10
SSC CHSL 09/08/2023 (4th Shift)
(a) 10 (b) 40 (c) 30 (d) 20 5 2
Q.80. The mean proportion of number
0.049 and 0.9 is:
SSC CHSL 10/08/2023 (1st Shift)
(a) 0.021 (b) 0.21 (c) 0.63 (d) 21
Q.81. The ratio of the father's age to his
son's age is 5 : 3. The product of the
numbers representing their ages is
960.The ratio of their ages after 6 years
will be:
SSC CHSL 11/08/2023 (1st Shift)
(a) 23 : 15 (b) 23 : 17
(c) 21 : 15 (d) 21 : 17
Q.82. Find the third proportion of P and
12, when 8, P , 16 and 18 are in
proportion.
SSC CHSL 11/08/2023 (2nd Shift)
(a) 16 (b) 8 (c) 18 (d) 12
Q.83. The total number of workers in a
company is 960. If the number of female
workers in the company is 420, then the
respective ratio of the total number of
male workers to the total number of
female workers in the company is:
SSC CHSL 11/08/2023 (3rd Shift)
(a) 7 : 9 (b) 16 : 9 (c) 16 : 7 (d) 9 : 7
Q.84. Given that x varies directly as y and
x = 45 when y = 9. What is the value of x
when y = 50 ?
SSC CHSL 17/08/2023 (1st Shift)
(a) 225 (b) 190 (c) 175 (d) 250
Q.85. If a : b = 3 : 7, then (2a + 3b): (3a +
2b) is:
SSC CHSL 17/08/2023 (2nd Shift)
(a) 27 : 23 (b) 23 : 29 (c) 21 : 29 (d) 21 : 23
Q.86. Divide ? 1488 among X, Y and Z. If
the shares are in the ratio X : Y = 4 : 5, Y :
Z = 7 : 6, then ?nd out the share of Z.
SSC CHSL 17/08/2023 (3rd Shift)
(a) ? 460 (b) ? 450 (c) ? 470 (d) ? 480
SSC CGL 2023 Tier - 1
Q.87. The ratio of the number of boys to
that of the girls in a school is 11 : 15. If
there are 200 more girls than boys in the
school, what is the number of boys in
that school ?
SSC CGL 14/07/2023 (4th shift)
(a) 550 (b) 750 (c) 506 (d) 605
Q.88. The ratio between the monthly
income and the expenditure of Vaidic is
8: 5. If his income increases by 20% and
his expenditure increases by 30%, then
?nd the percentage increase or decrease
in his monthly savings.
SSC CGL 14/07/2023 (4th shift)
(a) 5 % increase (b) 5 % decrease
2
3
2
3
(c) 3 % increase (d) 3 % decrease
1
3
1
3
Q.89. The ages of Gyanendra and Arbind
are in the ratio 6 : 5. If the sum of their
ages is 55 years, then what will be the
ratio of their ages after seven years from
now ? SSC CGL 14/07/2023 (4th shift)
(a) 5 : 6 (b) 37 : 32 (c) 32 : 37 (d) 6 : 5
Q.90. A bag contains ?550 in the form of
50p, 25p and 20p coins in the ratio 2 : 3 :
5. The difference between the amounts
that are contributed by the 50 p and the
20 p coins is:
SSC CGL 17/07/2023 (3rd shift)
(a) ?30 (b) ?20 (c) ?10 (d) ?0
Q.91. The third proportional to (x² - y²)
and (x - y) is:
SSC CGL 18/07/2023 (1st shift)
(a) (x - y) (b) (c) (d) (x + y)
?? - ??
?? + ??
?? + ??
?? - ??
Q.92. In a factory, 48% of the number of
male workers is equal to two-third of the
number of female workers. What is the
ratio of the number of males to that of
the females in the factory?
SSC CGL 18/07/2023 (2nd shift)
(a) 25 : 12 (b) 12 : 25 (c) 18 : 25 (d) 25 : 18
Q.93. Find the fourth proportional of 144,
192 and 216.
SSC CGL 18/07/2023 (4th shift)
(a) 361 (b) 288 (c) 324 (d) 289
Q.94. Two numbers are, respectively,
17% and 50% more than a third number.
The ratio of the two numbers is:
SSC CGL 19/07/2023 (4th shift)
(a) 27 : 25 (b) 39 : 50
(c) 19 : 11 (d) 29 : 25
Q.95. If a : b :: b : c, and b = 96, then
which of the following can be a possible
pair of values of a and c ?
SSC CGL 20/07/2023 (2nd shift)
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FAQs on SSC CGL Previous Year Questions (2023-18): Ratio & Proportion - SSC CGL Previous Year Papers
| 1. What is the basic concept of Ratio and Proportion in mathematics? |  |
Ans. The basic concept of Ratio and Proportion involves comparing two or more quantities. A ratio is a relationship between two numbers indicating how many times the first number contains the second. Proportion, on the other hand, states that two ratios are equal. For example, if a:b = c:d, then a, b, c, and d are in proportion.
| 2. How can I solve problems related to Ratio and Proportion in SSC CGL exams? | |
Ans. To solve Ratio and Proportion problems in SSC CGL exams, first, identify the quantities involved and their relationships. Set up the ratios according to the given information, and then use cross-multiplication or simplification to find the unknowns. Practice is key, so work on previous years' questions and sample papers.
| 3. What types of questions on Ratio and Proportion are commonly asked in SSC CGL exams? | |
Ans. Common types of questions include finding the ratio of two quantities, determining the value of unknowns in a proportional relationship, word problems involving sharing or distribution of quantities, and questions requiring simplification of ratios. Familiarity with these types will help in preparation.
| 4. Can you explain the difference between direct and inverse proportion? | |
Ans. Direct proportion means that as one quantity increases, the other also increases, maintaining a constant ratio. For example, if x is directly proportional to y, then x/y = k (a constant). Inverse proportion means that as one quantity increases, the other decreases, maintaining a constant product. For instance, if x is inversely proportional to y, then xy = k.
| 5. Are there any specific formulas for solving Ratio and Proportion problems? | |
Ans. Yes, some useful formulas include: For two quantities a and b, the ratio is expressed as a:b. If a:b = c:d, then a/b = c/d. For solving proportions, the cross multiplication method is used, where a:b = c:d implies a*d = b*c. Additionally, to simplify ratios, divide both terms by their greatest common divisor (GCD).
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