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?
Answer & explanation
Answer: (c) 20%
For a fixed job, the number of men is inversely proportional to the number of days. Cutting the days from 6k to 5k needs 6/5 times the men, which is a 20% increase.
- Work = men × days, so M × 6k = M′ × 5k.
- M′ = M × 6k/5k = (6/5)M; the k cancels.
- Increase = (6/5 − 1) × 100% = (1/5) × 100% = 20%.
- Check: with k = 1, 5 men for 6 days = 30 man-days = 6 men for 5 days, and 6 is 20% more than 5.
Remember · For fixed work, new men = old men × old days ÷ new days. Common factors like k cancel out.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·