A liquid mixture of methanol and water at boiling point is fed to a fractionating column at $200$ kmol$/$hr$.$ The mole fraction of methanol in the feed is $0\mathrm{.}20$ and the desired overhead $($distillate$)$ composition should contain $90$ mole percent of methanol and the bottoms produce $98$ mole$\%$ of water. A reflux ratio of $3\mathrm{.}2$ is to be used. Use the equilibrium data below and answer the following questions. x $00,10,20,30,40,50,6$ y $00,70,80,9$