# 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%.