A pipe can fill an overhead tank in 12 hours. But due to a leak at the bottom, it is filled in 18 hours. If the tank is full, how much time will the leak take to empty it?

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Accepted Answer

Let the capacity of the tank be 1 unit.

Rate of filling by pipe = 1/12 units per hour.
Rate of filling with leak = 1/18 units per hour.

Let the rate of leak be x units per hour (emptying rate).

Since leak reduces the filling rate:

(1/12) - x = 1/18

=> x = (1/12) - (1/18)

Find common denominator 36:

x = (3/36) - (2/36) = 1/36 units per hour.

So, leak empties 1/36 of the tank per hour.

Time taken by leak to empty the full tank = 1 / (1/36) = 36 hours.

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