Discussion Forum

Two pipes A and B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 minutes ?

Answer:

Explanation:

Let $B$ be closed after $x$ minutes. Then,

part filled by $(A+B)$ in $x$ min + part filled by $A$ in $(18-x)$ min $= 1$

$\Leftrightarrow x\left( \frac{1}{24}+\frac{1}{32}\right)+\left(18-x\right) \times\frac{1}{24}=1$

$\Leftrightarrow\frac{7x}{96}+\frac{18-x}{24}=1$

$\Leftrightarrow 7x+4(18-x)$ $=96$

$\Leftrightarrow 3x=24$ $\Leftrightarrow x=8$

Hence, $B$ must be closed after 8 minutes.