Question

10. A pipe can fill a cistern in 6 hours. Due to a leak in the bottom it is filled in 7 hours. When the cistern is

full, in how much time will it be emptied by the leak?
Multiple Choice Questions (MCQs)
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Answer 1

7 hours.

Explanation:

This is a rate problem. We can start by using the formula: Rate x Time = Quantity.

The rate at which the cistern is filled is the quantity of water in the cistern divided by the time it takes to fill it. So, the rate at which the cistern is filled is 1 (the cistern is full) / 6 hours = 1/6 cistern/hour.

Similarly, the rate at which the cistern is emptied by the leak is 1 (the cistern is full) / the time it takes to empty it. So, the rate at which the cistern is emptied by the leak is 1 (the cistern is full) / 7 hours = 1/7 cistern/hour.

Since we know the rate at which the cistern is filled and the rate at which it is emptied, we can find the time it takes for the cistern to be emptied by dividing 1 (the cistern is full) by the rate at which it is emptied.

Therefore, the cistern will be emptied in 1 / (1/7 cistern/hour) = 7 hour.