'A' pipe can fill a tank in x hours and another 'B' can empty in y ho…

 Total work = efficiency × time 

Time taken by them together to fill the tank =  \(\frac{xy}{y-x}\)   

                                                                               as,   ( y > x )

                                               OR 

 workdone by pipe A in filling the tank in 1 hour = \(\frac{1}{x}\)

workdone by pipe B in filling the tank in 1 hour = \(\frac{1}{y}\)

 Net workdone by pipe A and pipe B in filling the tank in 1 hour

= \(\frac{1}{x}\) - \(\frac{1}{y}\)

 = \(\frac{y-x}{xy}\)

then, full tank filled in = (\(\frac{xy}{y-x}\)) hours