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Tap A fills a tank in 6 hours, tap B in 8 hours, and drain C empties it in 12 hours. A is opened on the empty tank at 6 a.m., B at 7 a.m., C at 8 a.m., and A is closed at 9 a.m. At what time is the tank full?

Competition practicePipes & Cisterns
  • A11 a.m.
  • B1 p.m.
  • C10:40 a.m.
  • D5 p.m.

Step-by-Step Solution

In 24ths: 6–7: 4; 7–8: 7 (total 11); 8–9: 4+3−2 = 5 (total 16). From 9 a.m. only B and C: 3−2 = 1 per hour, so the last 8 take 8 h → 5 p.m.
Answer: D) 5 p.m.

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