Question

A cistern has three taps in all. two taps are used for filling the cistern and the third one is used to empty the cistern. the first two taps fill the cistern in 13 minutes and 11 minutes respectively. when all the three taps are open, the empty cistern is filled in 30 minutes. how long will the third tap (waste pipe) take to empty the cistern completely?

Answer 1

This is a question on proportions :

Let the inlet taps be A and B.

The outlet pipe to be C.

In one minute :

A fills 1/13 of the tank.

B fills 1/11 of the tank.

Let the time take by C to empty the tank be C.

Then the amount emptied in one minute is : 1/C

We can write this as follows :

In one minute the amount filled is :

1/13 + 1/11 - 1/C = 1/30

24/143 - 1/C = 1/30

-1/C = 1/30 - 24/143

-1/C = - 577/4290

1/C = 577/4290

C = 4290/577

C = 7.45 minutes