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% ✓ UPSC's answer
(d) 25%

Why the answer is (c)

• The total work is constant, so the product of the number of men and the number of days remains the same.

• Let the initial number of men be M, so the total work is M * 6k.

• To complete the same work in 5k days, let the new number of men be M'.

• Equating the work: M * 6k = M' * 5k, which simplifies to M' = (6/5)M.

• The increase in the number of men is M' - M = (6/5)M - M = (1/5)M.

• The percentage increase is ((1/5)M / M) * 100 = 20%.

Why the other options are wrong

(a) 10%: A 10% increase would result in a completion time of approximately 5.45k days, not 5k days.
(b) (50/3)%: A (50/3)% increase corresponds to a factor of 1.166, which does not match the required ratio of 1.2.
(d) 25%: A 25% increase would result in a completion time of 4.8k days, which is less than the required 5k days.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.