A tap A can fill a cistern in 4 hours and the tap B can empty the full cistern in 6 hours. If both the taps are opened together in the empty cistern, in how much time will the cistern be filled up?

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Solution

Time taken by tap A to fill the cistern = 4 hours.

Work done by tap A in 1 hour = 1/4ᵗʰ

Time taken by tap B to empty the full cistern = 6 hours.

Work done by tap B in 1 hour = -1/6ᵗʰ (since, tap B empties the cistern).

Work done by (A + B) in 1 hour (¹/₄ - ¹/₆) = (3 - 2)/12 = 1/12th part of the tank is filled.

Therefore, the tank will fill the cistern = 12 hours.

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