Time & Work- 2 - Free MCQ Practice Test with solutions, GATE ME General

Efficiency of A = 100 / 12 = 8.33%
Efficiency of B = 100 / 15 = 6.66%
Combined efficiency of A and B = 8.33 + 6.66 = 15%
Number of days taken by A and B, when working together = 100 / 15 = 
Note : Efficiency x Time period = Fixed amount of work
Also, in terms of percentage total work to be done is considered as 100% (in fraction it is 1), unless otherwise stated.
Alternatively : It can be done through unitary method, also.

►Efficiency of A = 20% = 100 / 5

►Efficiency of B = 10% = 100 / 10

►Efficiency of A,B and C = 50%

►∴ Efficiency of C = (Efficiency of A,B and C) – (Efficiency of A and B) = (50) - (20 + 10) = 20%

►∴ Number of days required by C to work alone = 100 / 20 = 5 days

►Alternatively: Go through options and satisfy the values.

(Since number of days are inversely proportional to the efficiency)
Now if A requires x days, so B requires 3x days.
∴ Difference of required days = (3x - x) = 2x = 10
    ► ⇒ x = 5
Hence the number of days required by
   ► B = 3x = 3 x 5 = 15 days

Efficiency of A + B = 33.33% = (100 / 3)

Ratio of efficiency of A and B = 3 : 1
∴ Efficiency of A = 
∴ Number of days taken by A = 4 = 100 /25
Alternatively :

∴ Difference in days = 2x = 8
 ► ⇒ x = 4 and 3x = 12

Therefore number of days taken by A, working alone = 4 days
Alternatively : 

Now, you can use the options, or solve the equations to get the value of x which is equal to 4.

Remember
Now,

Again, efficiency of Ganga, Jamuna and Saraswati
     = 100 / 1 = 100%
∴ Efficiency of Ganga = 
Efficiency of Saraswati = 
Now, number of days taken by Ganga
     = 100 / 50 = 2
Number of days taken by Saraswati
     = 100 / 33.33 = 3
∴ Difference in number of days taken by Ganga and Saraswati
     = 3 - 2 = 1 day

Work done in 11 days = 11 / 30
Rest work = 19 / 30
1 day's work of A = 
Total number of days required to complete the whole work alone.

∴ Number of days required by Asha to finish the work alone = 20
  ► ∴ (4 x = 4 x 5)
(Alternatively, from percentage change graphic, number of days taken by Asha will be 20% less than Usha, if efficiency of Asha is 25% more than Usha)
Now, since Asha and Usha did work together for last 5 days = 5 x 9 = 45%
(Since efficiency of Asha = 5% and Usha's efficiency = 4%)
It means Asha completed 55% work alone
∴ Number of days taken by Asha to complete 55% work = 55 / 5 = 11

Efficiency of Chandni = 11.11%
Efficiency of Divakar = 8.33%
They do 19.44% work in 2 days.
∴ They need 10 days to do 97.22% work,
Now the rest work (2.78) was done by Chandni in 2.78 / 11.11 = 1 / 4 days
Therefore total number of days required = 
Alternatively :
Chandni's one day's work = 1 / 9
Divakar's one day's work = 1 / 12
Chandni's and Divakar's (1 + 1) = 2 day's work = 1 / 9 + 1 / 12 = 7 / 36
So, in 10 days they do = 
So, the remaining work will be done by Chandni = 
Thus total number of required days = 
Hint

Let X be the initial number of men then,
According to the question,
4X = X + (X - 20) + (X - 40) + (X - 60) + (X - 80) + (X - 100) + (X - 120)
⇒ 4X = 7X - 420
⇒ 3X = 420
⇒ X = 420/3
⇒ X = 140 men

   ► 6 / 8 = 3 / 4
In 3 days A,B,C do 3 / 8 work,
In 6 days A,B,C do 3 / 4 work
Rest work = 1 / 4, which is less than 3 / 8, On the 7th day, 1 / 6 more work will be done by A
Now rest work = 
Now, this rest work (1 / 12) will be done by B in 1 complete day.
Thus, total number of days = 6 + 1 + 1 = 8 days.
Alternatively : Efficiency of A = 16.66% , Efficiency of B = 8.33% , Efficiency of C = 12.5%
Efficiency of A + B = 25% , Efficiency of A + B + C = 37.5%
In 3 days A,B,C completes 37.5% work, In 6 days A,B,C completes 75% work
Rest work = 25%
This 25% work will be completed by A and B in next 2 days, Thus total 6 + 2 = 8 days are needed.

A + B = 70%
B + C = 50%

⇒ B = 20% , A = 50% and C = 30%
Hence, A is most efficient.

  ► ∴ 0.8k = 24 ⇒ k = 30
Thus Sharma requires 30 days, to complete the work, alone.

M x D = 10 x 20 = 200
Man-days New Man-days = (20 x 2) x x
   ► 200 = 20 x 2 x x
   ► x = 5 days
or M₁D₁ = M₂D₂
   ► 10 x 20 = (20 x 2) x x
   ► ⇒ x = 5

Go through options. Consider option (c)
 ► 30 x 20 = 30 x 6 + 21 x 20
 ► 600 = 600,
Hence presumed option is correct.

Alternatively :
 ► ​30 x 20 = 30 x x + 21 x (26 - x )
 ► ⇒ x = 6

Efficiency (per minute) of Modi = 4 copies/min
Efficiency of Modi and Xerox together = 10 pages/min
∴ Efficiency of Xerox alone = 10 - 4 = 6 pages/min
∴ Mr. Xerox needs 6 minutes to copy 36 pages.

6C + 2 M = 6 days
 ► ⇒ 36C + 12 M = 1 day
Again 1M = 2C
 ► ∴ 36 + 12 x 2 = 1 day
60 children can do the work in 1 day Now,
 ► 5 men = 10 children
∴ 10 children can do the work in 6 days.

Efficiency of A = 6.66% , Efficiency of B = 5.55% , Efficiency of A + B + C = 16.66%
∴ Efficiency of C = 4.44%
Now, number of days required by C = 

Correct Answer :- B

Explanation : A = 15 days

B = 18 days

C = 6 days

Taking LCM, we get 180

Efficiency of A = 12

Efficiency of B = 10

Efficiency of A+B+C = 6

A.T.Q

=> (10/30)*27000

= 9000

In 1 hour 314 weavers weave = 6594 x 6
shawls In 1 hour 1 weavers weave  = = 126 shawls

Equate the man-days
For 20 km road, 20 x 20 = 400 man-days are required
∴ For 40 km road 800 man-days are required So, 800 = 40 * x
  ► ⇒ x = 20

Efficiency of a man : woman : girl = 6 : 3 : 1
∴ Share of a woman and girl = 
= 

Let x kg of oil is used for eating purpose, daily, then
   ► (x + 11) x 50 = + 15 x 45
   ► x = 25
∴ Total quantity of oil = (25 + 11) x 50 = 1800
∴ Required number of days = 1800 / 25 = 72
 

Correct Answer :- d

Explanation : LCM(20,25,30)=300

Suppose capacity of the tank is 300 litre.

Quantity filled by tap A in 1 hour 

= 300/20

= 15 litre.

Quantity filled by tap B in 1 hour = 300/25

= 12 litre.

Quantity emptied by tap C in 1 hour = 300/30

= 10 litre.

In every three hour, 15 + 12 − 10 = 17 litre is filled.

In 45 hours,  

17 × 15 = 255 litre is filled.

Remaining quantity to be filled = 300 − 255 = 45 litre.

In next 3 hour, 17 more litre is filled.

Remaining quantity to be filled = 45 − 17 = 28 litre.

In next 2 hour hour, 15 + 12 = 27 more litre is filled.

Remaining quantity to be filled = 28 − 27 = 1 litre.

But in next 1 hour, 10 litre is emptied.

Remaining quantity to be filled = 1 + 10

= 11 litre.

Pipe A fills this remaining quantity in 11/15hour (i.e, in 44 minutes).

Therefore, the tank is filled in 51 hour 44 minutes

In ideal case :
Time taken to fill the half tank by A and B = 50 / 41.66 = 6 / 5 hours
Time taken by A,B and C to fill rest half of the tank = 50 / 16.66 = 3 hours
Total time = 
In second case :
Time taken to fill 3 / 4 tank by A and B = 75 / 41.66 = 9 / 5 hours
Time taken by A,B and C to fill rest 1 / 4 tank = 25 / 16.66 = 3 / 2 hours
Total time = 9 / 5 + 3 / 2 = 3 hours 18 minutes
Therefore, difference in time = 54 minutes