UPSC Prelims 2024 · CSAT
Question 7: Basic Numeracy
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?
AnswerUPSC’s answer is (c).
The work is fixed, so the number of men is inversely proportional to the number of days. Men × days is constant: M × 6k = M′ × 5k, so M′ = 6M/5 = 1.2M. That is a 20 percent increase. The value of k cancels out, so it does not matter. Remember: for the same work, if time falls from T1 to T2, men must rise by (T1 − T2)/T2, here (6 − 5)/5.
Why each option is right or wrong
- (a) Wrong. A 10% increase gives 6k ÷ 1.1, about 5.45k days, not 5k.
- (b) Wrong. 50/3 percent means 7/6 of the men, giving 36k/7, about 5.14k days, not 5k.
- (c) Right. 6/5 = 1.2, so the men must rise by 20%.
- (d) Wrong. A 25% increase gives 6k ÷ 1.25 = 4.8k days, not 5k.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.