Question

Two pipes $M$ & $N$ can fill a system 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,
$x(\frac{1}{12}+\frac{1}{16})+(9-x)\frac{1}{12}=1$
$\Rightarrow x=16\times \frac{3}{12}$
$\Rightarrow x=4hrs=240$ minutes