Pipe A can fill a cistern in 10 hours, pipe B in 15 hours, and pipe C can empty it in 30 hours. All three pipes are opened together. After 6 hours, pipe A is closed, but B and C continue working. How much total time will it take to completely fill the cistern?
12 hours
Rates: A fills at \(\tfrac{1}{10}\), B fills at \(\tfrac{1}{15}\), C empties at \(\tfrac{1}{30}\) per hour.
Combined rate for the first 6 hours: \(\tfrac{1}{10}+\tfrac{1}{15}-\tfrac{1}{30} = \tfrac{3+2-1}{30} = \tfrac{2}{15}\) per hour.
Work done in 6 hours: \(6\times\tfrac{2}{15} = \tfrac{4}{5}\). Remaining work: \(\tfrac15\).
After A closes, B and C combined rate: \(\tfrac{1}{15}-\tfrac{1}{30} = \tfrac{1}{30}\) per hour.
Time for remaining work: \(\dfrac{1/5}{1/30} = 6\) hours.
Total time: \(6+6 = 12\) hours.
Hence, it takes 12 hours in total to completely fill the cistern.
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Important Questions from Pipe and Cistern
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