Question

Two pipes $A$ and $B$ can fill a cistern in $37\frac{1}{2}$ minutes and $45minutes$ respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the $B$ is turned off after :

• A. $5min$
• B. $9min$
• C. $10min$
• D. $15min$

Answer 1

The correct option is B $9min$

Let B be turned off after x minutes. Then,
Part filled by $(A+B)$ in x min. $+$ Part filled by A in $(30-x)$min. $=1$.
$\therefore x\left(\frac{2}{75}+\frac{1}{45}\right)+(30-x).\frac{2}{75}=1$
$\Rightarrow \frac{11x}{225}+\frac{(60-2x)}{75}=1$
$\Rightarrow 11x+180-6x=225$.
$\Rightarrow x=9$.