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