Discussion Forum

A water tank is $\frac{2}{5}$ full. Pipe $A$ can fill a tank in $10$ minutes and pipe $B$ can empty it in $6$ minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

Answer:

Explanation:

Clearly, pipe $B$ is faster than pipe $A$ and so, the tank will be emptied.

Part to be emptied  $=\frac{2}{5}$.

Part emptied by  $(A+B)$ in $1$ minute  $=\left(\frac{1}{6}-\frac{1}{10}\right)$  $=\frac{1}{15}$.

$\therefore$ $\frac{1}{15}:\frac{2}{5}::1:x$ or  $x=\left(\frac{2}{5}\times 1\times 15\right)$  $=6$ min.

So, the tank will be emptied in 6 min.