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