Multiple choice

Inlet pipe A can fill a cistern in 32 hours, whereas outlet pipe B can drain the filled cistern in 40 hours. The two pipes are opened together when the cistern is empty, but the outlet pipe is closed when the cistern is three-quarters full. How many hours will it take in all to fill the cistern?

  1. 128

  2. 120

  3. 80

  4. 62
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Both pipes are opened together until the cistern is 3/4 full. The net filling rate when both are open is 1/32 - 1/40 = 1/160 cistern per hour. Time to fill 3/4 = (3/4) / (1/160) = 120 hours. For the remaining 1/4, only inlet pipe A works at rate 1/32, taking (1/4) / (1/32) = 8 hours. Total time = 120 + 8 = 128 hours.

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