A pipe can fill a cistern in 10 hours. Due to a leak in the bottom it is filled in 12 hours. When the cistern is full, in how much time will it be emptied by the leak?

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Solution

$When there is no leakage, the pipe can fill the cistern in 10 hours . Thus, the pipe can fill \frac{1}{10} th part of the cistern in 1 hour . When there is leakage, the pipe can fill the cistern in 12 hours . Therefore, in case of leakage, the pipe can fill \frac{1}{12} th part of the cistern in 1 hour . Thus, in one hour, due to leakge, (\frac{1}{10} - \frac{1}{12}) th or \frac{1}{60} th part of the cistern is emptied . Hence, the cistern will be emptied by the leakage in 60 hours .$

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