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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?

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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.

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