A cistern which could be filled in $9$ hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full, in what time will the leak empty it ?

The filling pipe's rate is 1/9 per hour, while the combined rate with the leak is 1/10 per hour. The leak's rate equals the difference, which is 1/9 - 1/10 = 1/90 per hour. Therefore, the leak alone will empty the full cistern in 90 hours. The result is 90 hours.

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