Question:
A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak?
Solution:
A pipe can fill a cistern in 9 hours.
Part of the cistern filled by the pipe in one hour $=\frac{1}{9}$
Let the leak empty the cistern in $\mathrm{x}$ hours.
Part of the cistern emptied by the leak in one hour $=-\frac{1}{x}$ (The leak drains out the water)
Considering the leak, the tank is filled in 10 hours.
Part of the tank filled in one hour $=\frac{1}{10}$
Therefore,
$\frac{1}{9}-\frac{1}{\mathrm{x}}=\frac{1}{10} \text { or, } \frac{1}{\mathrm{x}}=\frac{1}{9}-\frac{1}{10}=\frac{10-9}{90}=\frac{1}{90} \mathrm{x}=90$
The leak will empty the filled cistern in 90 hours.