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Question

A pump can fill a tank with water in 2 hours. Because of a leak, it took 3 hours to fill the tank. The leak can drain all the water of the tank in:

A
4 hours
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B
6 hours
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C
2 hours
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D
3 hours
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Solution

The correct option is B 6 hours
Let the volume of the tank be v litres.
Now, the tank can be filled by a pump in 2 hours, then, it can fill v2 in 1 hour
Similarly, the tank can be filled with leakage in 3 hours, then, with a leak, the pump can fill v3 in 1 hour.
Thus, the work done by leakage is v2v3 in 1 hour.
=v6
Thus the tank will v litres as volume can be completely emptied by the leakage in 6 hours.

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