Question

A cistern has a leak which would empty it in 8 hours. A tap is turned on which admits 6 litres a minute into the cistern and it is now emptied in 12 hours. How many litres does the cistern hold?

Answer 1

Answer:

8640 litres

Step-by-step explanation:

Let x be the number of litres that the cistern holds.

Leak rate = x / 8  litres / hour

Tap rate = 6 litres / min  =  360 litres / hour

Combined rate = ( x / 8 - 360 ) litres / hour  =  x / 12  litres / hour

=> 3x - 24×360 = 2x

=> x = 24×360 = 8640

Answer 2

The capacity of the tank = 8640 litres