Previous Year Topic Wise Questions With Solutions: Time & Work | CSAT Preparation - UPSC PDF Download

Ans: (b)
X can complete one-third of a certain work in 6 days. 
So, X can complete total work in 6 × 3 = 18 days 
Y can complete one-third of a certain work in 8 days. 
So, Y can complete total work in 8 × 3 = 24 days 
Z can complete three-fourth of a certain work in 12 days. 
So, Z can complete total work in (4/3) × 12 = 16 days 
Let the total amount of work be the LCM of 16, 18 and 24, i.e. 144 units 
So, efficiency of X = (144/18) = 8 units/day 
Efficiency of Y = (144/24) = 6 units/day 
Efficiency of Z = (144/16) = 9 units/day 
Efficiency of X, Y and Z together = (8 + 6 + 9) units/day = 23 units/day 
Work done by Y in 26/3 days = (26/3) x 6 = 52 units 
Remaining work = 144 - 52 = 92 units 
Time required to complete this work when they work together = 92/23 = 4 days 
So, n = 4

Ans: (d)
20 X pipes can fill 70% tank in 14 minutes. 
So, 20 X pipes can fill 100% tank in (14/70) × 100 = 20 minutes
10 Y pipes can fill 3/8^th of the tank in 6 minutes.
So, 10 Y pipes can fill 100% tank in [6/(3/8)] × 100 = 16 minutes 
16 Z pipes can empty 50% tank in 20 minutes.
So, 16 Z pipes can empty 100% tank in 40 minutes.
As per the question, X and Y work at half their capacity, while Z work at full capacity. 
So, Set X pipes can fill the tank in 40 minutes. 
Set Y pipes can fill the tank in 32 minutes.
And, Set Z pipes can empty the tank in 40 minutes.
We can see that pipes X and Z will eliminate each other’s efforts. 
So, the question boils down to this: In how much time will Y fill 50% of the tank?
As Y can fill the entire tank in 32 minutes, it will fill half the tank in 16 minutes.

Ans: (c)
Let the number of men in the first and second instances be m and n respectively. 
So, man-days required = 6k × m = 5k × n
Or 6m = 5n Or n = (6/5)m Or n = 1.2 m
Or n = m + 20% of m
So, the number of men need to be increased by 20%.

Ans: (c)
X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. 
Now, to finish the work in minimum possible time, we need to ensure that X is utilized the most, as he’s the most efficient worker. 
So, we will use X alternatively every second hour. We will also start with him.
So, the sequence of their working will be X, (Y or Z), X, (Y or Z), X, …..and so on.
X can complete the work in 6 hours. So, in one hour he can complete 16.67% of the work.
Similarly, Y (or Z) can complete the work in 8 hours. So, in one hour he can complete 12.5% of the work.
Now, X + Y + X + Y + X + Y = 3X + 3Y = 50 + 37.5 = 87.5%
Now, 12.5% of the work is left and it’s X’s turn to do it.
X can do it in (12.5/16.67) hours, i.e. 0.75 hours, or 45 minutes.
So, the entire task can be done by them in the minimum possible time of 6 hours 45 minutes.

Ans: (d)
Since the comparative efficiencies of man and women are not known, we cannot determine the time taken by 12 men and 24 women to complete the given work.
Hence, the data is inadequate to draw any conclusion.