Question
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?
Answer: Option D
Net part filled in 1 hour
$$\eqalign{
& {\text{= }}\left( {\frac{1}{x} - \frac{1}{y}} \right) \cr
& = \left( {\frac{{y - x}}{{xy}}} \right) \cr} $$
∴ The tank will be filled in
$$ = \left( {\frac{{xy}}{{y - x}}} \right)\,\,{\text{hours}}$$
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Net part filled in 1 hour
$$\eqalign{
& {\text{= }}\left( {\frac{1}{x} - \frac{1}{y}} \right) \cr
& = \left( {\frac{{y - x}}{{xy}}} \right) \cr} $$
∴ The tank will be filled in
$$ = \left( {\frac{{xy}}{{y - x}}} \right)\,\,{\text{hours}}$$
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