Question

A water tank is two-fifths full. The pipe $A$ can fill a tank in $10minutes$ and the pipe $B$ can empty it in $6minutes.$ If both the pipes are open, how long will it take to empty or fill the tank completely?

• A. $6min$ to empty
• B. $6min$ to fill
• C. $9min$ to empty
• D. $9min$ to fill

Answer 1

The correct option is B

$6min$ to fill

Since the pipe $B$ is faster, the tank will be emptied.

Work done by pipe $A$ in $1min=\frac{1}{10}$

Work done by pipe $B$ in $1min=\frac{1}{6}$

Total work when $A$ and $B$ are opened $=\frac{1}{6}–\frac{1}{10}$

$$\begin{gathered} =\frac{4}{60} \\ =\frac{1}{15} \end{gathered}$$

Part emptied in by$A$ and $B$ in $1min=\frac{1}{15}$

Time is taken to empty $\frac{2}{5}$ the tank $=\frac{{\displaystyle \frac{2}{5}}}{{\displaystyle \frac{1}{15}}}$

$=6min$

Hence, the time taken to empty $\frac{2}{5}$ of the tank is $6min.$to fill.

Hence, the correct option is B.