A column is to be designed to separate acetone$-$methanol mixture at $L$ atm. The feed contains $40$ mole $\%$ acetone and $60$ mole $\%$ methanol, and it enters the column as a boiling$-$liquid mixture. The bottom is to contain $10$ mole $\%$ acetone and $90$ mole $\%$ methanol, and the distillate contains $65$ mole $\%$ acetone and $35$ mole $\%$ methanol. A reflux ratio of $4$kmo$\frac{l}{k}$mol product is used.

Using the equilibrium curve diagam of acetone$-$methanol system at I atm in below table and determine by Lewis$-$Sorel method

a$)$ The amount of distillate and bottom products

b$)$ The equations of rectifying and stripping sections the equilibrium vapor and liquid compositions of the third tray $($from top column$).$

$\backslash$table$[[T[K],x_1,y$