Question

A cistern has a leak which can empty it in 4 hours. A pipe which admits 20 liters of water per hour into the cistern is turned on, and now the cistern is emptied in 6 hours. What is the capacity of the cistern?​

Answer 1

The capacity of the cistern is 240 liters.

Step-by-step explanation:

To find the capacity of the cistern, we need to determine the rate at which water is being emptied with the leak and the rate at which water is being filled with the pipe.

Let's assume the capacity of the cistern is C liters.

The leak can empty the cistern in 4 hours, so the rate at which water is being emptied is C/4 liters per hour.

The pipe admits 20 liters of water per hour, so the rate at which water is being filled is 20 liters per hour.

With the pipe turned on, the cistern is emptied in 6 hours, so the rate at which water is being emptied and filled is the same. We can set up the equation:

C/4 - 20 = C/6

Multiplying through by 12 to eliminate fractions:

3C - 240 = 2C

C = 240

Therefore, the capacity of the cistern is 240 liters.