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.