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.

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