Question

A cistern has two pipes. One pipe can fill it with water in $8$ hours and the other can empty it in $5$ hours. In how many hours will the cistern be emptied if both the pipes are opened together when ${\left(\frac{3}{4}\right)}^{th}$ of the cistern is already full of water.

• A. $13\frac{1}{3}$ hours
• B. $10$ hours
• C. $6$ hours
• D. $3\frac{1}{3}$ hours

Answer 1

The correct option is B $10$ hours

Part of the tank filled by the first pipe in $1$ hour $=\frac{1}{8}$
Part of the tank emptied by the second pipe in $1$ hour $=\frac{1}{5}$
$\therefore$ Part of the tank emptied when both the pipes are opened together $=\frac{1}{5}-\frac{1}{8}=\frac{3}{40}$
$\therefore \frac{3}{40}$ part of the tank is emptied in $1$ hour
$\therefore \frac{3}{4}$th of the tank will be emptied in $\left(\frac{40}{3}\times \frac{3}{4}\right)$ hours $=10$ hours.