A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills 3/8th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set (Z) are open, then how long will it take to fill 50% of the tank?
Answer & explanation
Answer: (d) 16 minutes
Each X-pipe fills 1/400, each Y-pipe fills 1/160 and each Z-pipe empties 1/640 of the tank per minute. With 10 X-pipes, 5 Y-pipes and 16 Z-pipes open, the X and Z effects cancel (1/40 each), leaving 1/32 per minute, so half the tank takes 16 minutes.
- Take the tank as 1. Set X: 20 pipes fill 0.7 in 14 minutes, so one pipe fills 0.7 ÷ (14 × 20) = 1/400 per minute.
- Set Y: 10 pipes fill 3/8 in 6 minutes, so one pipe fills (3/8) ÷ 60 = 1/160 per minute.
- Set Z: 16 pipes empty 1/2 in 20 minutes, so one pipe empties (1/2) ÷ 320 = 1/640 per minute.
- Open pipes: 10 of X fill 10/400 = 1/40; 5 of Y fill 5/160 = 1/32; all 16 of Z empty 16/640 = 1/40 per minute.
- Net rate = 1/40 + 1/32 − 1/40 = 1/32 of the tank per minute.
- Time for 50% = (1/2) ÷ (1/32) = 16 minutes.
Remember · With sets of pipes, find the rate of one pipe first, then multiply by the number open; watch for rates that cancel.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·