CSAT 2024

Q. A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5K days?

a) 10%
b) (50/3)%
c) 20%
d) 25%
Correct answer: c) 20%

Question from UPSC Prelims 2024 CSAT

Explanation : 

Let’s approach this step-by-step:

1) Let’s say the original number of men is x.

2) We can express the relationship between men, days, and work as:
(Number of men) × (Number of days) = (Amount of work)

3) For the original scenario:
x × 6k = Amount of work

4) For the new scenario, let y be the new number of men:
y × 5k = Amount of work

5) Since the amount of work is the same in both cases:
x × 6k = y × 5k

6) We can express y in terms of x:
y = (x × 6k) / 5k = (6/5)x

7) The increase in the number of men is:
y – x = (6/5)x – x = (1/5)x

8) To express this as a percentage:
((1/5)x / x) × 100 = (1/5) × 100 = 20%

Therefore, the number of men should be increased by 20%.

The correct answer is c) 20%.

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