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

1(x - y) hours
2(y - x) hours
3^xy/_{x - y} hours
4^xy/_{y - x} hours

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Net part filled in 1 hour \\ = (\frac{1}{x} - \frac{1}{y}) = (\frac{y - x}{x y}) \\ ∴ The tank will be filled in \\ = (\frac{x y}{y - x}) hours \end{aligned}

$\eqalign{ & {\text{Net part filled in 1 hour}} \cr & {\text{ = }}\left( {\frac{1}{x} - \frac{1}{y}} \right) = \left( {\frac{{y - x}}{{xy}}} \right) \cr & \therefore {\text{The tank will be filled in }} \cr & {\text{ = }}\left( {\frac{{xy}}{{y - x}}} \right)\,{\text{hours}} \cr}$