A cistern has a hole at the bottom through which water leaks. A tap can fill the cistern in 7 hours and the hole at the bottom can empty the fully filled cistern in 8 hours. If both the tap and the hole are open, then what will be the time taken to completely fill the empty cistern?
56 hours
In 1 hour the tap fills \(\dfrac{1}{7}\) of the cistern.
In 1 hour the hole empties \(\dfrac{1}{8}\) of the cistern.
Net part filled in 1 hour = \(\dfrac{1}{7}-\dfrac{1}{8}=\dfrac{8-7}{56}=\dfrac{1}{56}\).
Time to fill the whole cistern = reciprocal of the net rate = \(56\) hours.
Hence, the cistern is completely filled in 56 hours.
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