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?
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, $\left(\frac{1}{10}-\frac{1}{12}\right)$ th or $\frac{1}{60}$ th part of the cistern is emptied.
Hence, the cistern will be emptied by the leakage in 60 hours.