24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
Answer & explanation
Answer: (d) Data is inadequate to draw any conclusion
The answer depends on how a man’s work rate compares with a woman’s, and that is not given. Equal rates give exactly 30 days, faster men give more than 30 and faster women fewer — so the data are inadequate.
- Let a man do m units and a woman w units of work a day. Work = 30 × (24m + 12w).
- Days for 12 men and 24 women = 30(24m + 12w)/(12m + 24w) = 30(2m + w)/(m + 2w).
- If m = w this is 30 days; if m > w it is more than 30; if m < w it is less than 30.
- The relation between m and w is not given, so no conclusion can be drawn. Option (c) fails because it leaves out the possibility of exactly 30 days.
Remember · In time-and-work items with two kinds of workers, you need their relative efficiency before you can swap one for the other.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·