Three pipes, A, B, and C are capable of filling a tank in 6, 8, and 12 hours, respectively. When all three pipes are opened toget…

Question

Three pipes, A, B, and C are capable of filling a tank in 6, 8, and 12 hours, respectively. When all three pipes are opened together, they operate for 2 hours before pipe C is closed. How much additional time will it take to completely fill the tank after that?

1. A. 6/7 hours (Correct answer)
2. B. 5/6 hours
3. C. 3/5 hours
4. D. 9/2 hours

Correct Answer

Option A — 6/7 hours

Detailed Solution & Explanation

The correct answer is 6/7 hours.

Key Points

• All three rates: 1/6 + 1/8 + 1/12 = 9/24 = 3/8 per hour, so in 2 hours they fill 2 × 3/8 = 3/4. Remaining = 1/4. With C closed, A + B = 1/6 + 1/8 = 7/24 per hour.
• Time = (1/4) ÷ (7/24) = (1/4) × (24/7) = 6/7 hours.
• Compute the filled fraction before the change, then the remaining work divided by the new (reduced) rate.