Question

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

• A. $9$ minutes
• B. $45$ minutes
• C. $10$ minutes
• D. $15$ minutes

Answer 1

The correct option is A $9$ minutes

Let pipe $B$ be turned off after $x$ minutes.
Then, part filled by $A$ in $30$ minutes $+$ part filled by $B$ in $x$ minutes $=1$
$\frac{2}{75}\times 30+x\times \frac{1}{45}=1$
$\Rightarrow \frac{4}{5}+\frac{x}{45}=1$
$\Rightarrow 36+x=45$
$\Rightarrow x=9$
So, the cistern will be filled in just half an hour, if $B$ is turned off after $9$ minutes.