A pipe can fill a cistern in 9 hours.

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.