A pipe can fill a cistern in: 9 hours

Let a leak empty the cistern in: X hours

Due to the leak time taken to fill the cistern : 10 hours

Part of the cistern filled by pipe in one hour: \(\frac{1}{9}\)

Part of the cistern emptied by leak in one hour: \(\frac{1}{x}\)

X = 90 hours

**Therefore the leak will empty the cistern in 90 hours.**