Practicing Success
'A' pipe can fill a tank in x hours and another 'B' can empty in y hours. In how many hours they together fill it if (y > x)? |
(x - y) hours (y - x) hours (\(\frac{xy}{x\;-\;y}\)) hours (\(\frac{xy}{y\;-\;x}\)) hours |
(\(\frac{xy}{y\;-\;x}\)) hours |
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 |