Discussion Forum

A large tanker can be filled by two pipes $X$ and $Y$ in $60$ minutes and $40$ minutes respectively. How many minutes will it take to fill the tanker from empty state if $Y$ is used for half the time and $X$ and $Y$ fill it together for the other half?

Answer:

Explanation:

Part filled by $(X+Y)$ in $1$ minute $=\left(\frac{1}{60}+\frac{1}{40}\right)$ $=\frac{1}{24}$.

Suppose the tank is filled in $x$ minutes.

Then, $\frac{x}{2}\left(\frac{1}{24}+\frac{1}{40}\right)$  = 1.

$\Rightarrow\frac{x}{2}\times\frac{1}{15}$ $=1$

$\Rightarrow x=30$ min.