Question

Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern? 

(a) 110 minutes 

(b) 100 minutes 

(c) 120 minutes 

(d) 90 minutes

Answer 1

(b) 100 minutes

Let the third pipe empty the whole cistern in x minutes.

\(\therefore\) \(\frac{1}{60}+\frac{1}{75}\) - \(\frac{1}{X}\) = \(\frac{1}{50}\)

\(\Rightarrow\) \(\frac{1}{X}\) = \(\frac{1}{60}+\frac{1}{75}-\frac{1}{50}\) = \(\frac{5+4-6}{300}\) = \(\frac{3}{300}\) = \(\frac{1}{100}\)

The third pipe can empty the cistern in 100 minutes