# A pipe can fill a tank in ‘x’ hours and another pipe can empty it in ‘y’ hours (y > x). If both the pipes are open, in how many hours will the tank be filled?

A pipe can fill a tank in ‘x’ hours and another pipe can empty it in ‘y’ hours (y > x). If both the pipes are open, in how many hours will the tank be filled?
[A](y – x) hours
[B](x – y) hours
[C]$\frac{xy}{y-x} hours$
[D]$\frac{xy}{x-y} hours$

$\frac{xy}{y-x} hours$
Part of the tank filled in 1 hour = $\frac{1}{x}$
Part of the tank emptyied in 1 hour = $\frac{1}{y}$
Part of the tank filled in 1 hour when both are opened = $\frac{1}{x}-\frac{1}{y}= \frac{y-x}{xy}$
∴ Tank will be filled in $\frac{xy}{y-x}$ hours
Hence option [C] is the right answer.