Question

Two pipes $M$ & $N$ can fill a cistern in $12$ & $16$ hrs respectively. If both the pipes are opened together, then after how many minutes $N$ should be closed so that the tank is full in $9$ hrs.

Answer 1

Let $N$ be closed after $x$ hrs

Then from the question, we have
$x(\frac{1}{12}+\frac{1}{16})+(9-x)\frac{1}{12}=1$
$\Rightarrow x$ $=$ $16\times \frac{3}{12}$
$\Rightarrow x$ $=$ $4$ hrs $=$ $240$ minutes