Two pipes P and Q are opened together to fill a tank. Both the pipes fill the tank in time [math]x.[/math] If P separately took [math]16[/math] minutes more time than [math]x[/math] to fill the tank and Q separately took [math]36[/math] minutes more time than [math]x[/math] to fill the tank, then find the value of [math]x.[/math]It is assumed that the unit of [math]x[/math] is also minutes.In such problem determine the quantity filled by P and Q in one unit time.It is given that the time taken by P and Q to fill the tank separately are [math]x+16[/math] and [math]x+36[/math] minutes respectively.[math]Rightarrowqquad[/math] In [math]1[/math] minute P and Q separately fill [math]frac{1}{x+16}[/math] and [math]frac{1}{x+36}[/math] part of the tank respectively.[math]Rightarrowqquad[/math] In [math]1[/math] minute P and Q to together fill [math]frac{1}{x+16}+frac{1}{x+36}[/math] part of the tank.It is given that in [math]x[/math] minute P and Q together fill the tank completely.[math]Rightarrowqquad left(frac{1}{x+16}+frac{1}{x+36}right)x=1 qquadRightarrowqquad left(frac{2x+52}{(x+16)(x+36)}right)x=1.[/math][math]Rightarrowqquad (2x+52)x=(x+16)(x+36)qquadRightarrowqquad 2x^2+52x=x^2+52x+576.[/math][math]Rightarrowqquad x^2=576 qquadRightarrowqquad x=24[/math] minutes.