Question

Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in 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. 90 min
• B. 100 min
• C. 110 min
• D. 120 min
• E. 130 min

Answer 1

The correct option is B

100 min

Work done by the third pipe in 1 min - $=\frac{1}{50}-\left(\frac{1}{60}+\frac{1}{75}\right)=\left(\frac{1}{50}-\frac{3}{100}\right)=-\frac{1}{100}$ [- ve sign means emptying]

$\therefore$ The third pipe alone can empty the cistern in 100 min.