Project ForgeTwo pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is _____.
- A13.50
- 14.50
- C15.50
- D16.50
Explanation
Phase 1 (P+R open, 4 hours): combined rate = 1/6-1/12 = 1/12 per hour; filled = 4/12 = 1/3. Phase 2 (Q+R open, 6 hours): combined rate = 1/9-1/12 = 1/36 per hour; filled = 6/36 = 1/6. After 10 hours, total filled = 1/3+1/6 = 1/2, remaining = 1/2. Phase 3 (R now closed, only Q open): rate = 1/9 per hour; time to fill remaining 1/2 = (1/2)/(1/9) = 4.5 hours. Total time = 10 + 4.5 = 14.5 hours.
Source: GATE ME 2019 Session 2 (Set 3) (2019)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.