Discussion Forum

Two pipes $A$ and $B$ can fill a tank in $36$ min and $45$ min respectively. A water pipe $C$ can empty the tank in $30$ min. First $A$ and $B$ are opened. After $7$ minutes, $C$ is also opened. In how much time, the tank is full ?

Answer:

Explanation:

Part filled in $7$ min $=7\left( \frac{1}{36}+\frac{1}{45}\right)$ $=\frac{7}{20}$

Remaining part $=\left( 1- \frac{7}{20}\right)$ $=\frac{13}{20}$

Net part filled in $1$ min. when $A$, $B$ and $C$ are opened $=\left(\frac{1}{36}+\frac{1}{45}-\frac{1}{30}\right)$ $=\frac{1}{60}$

Now, $\frac{1}{60}$ part is filled in $1$ min.

$\frac{13}{20}$ part is filled in $\left(60\times\frac{13}{20}\right)$ $=39$ min

Total time taken to fill the tank $=(39+7)$ min = 46 min.