$($b$)$ A continuous distillation column is fed with benzene, toluene mixture at its boiling point containing $35$ mole$\%$ benzene. The top product is to contain $95$ mole$\%$ of benzene and the bottoms are not to contain more than $5$ mole$\%.$ The reflux ratio is to be $3\mathrm{.}0.$ If the plate efficiency is $60\%,$ determine the number of plate and the position of the feed plate. The following $x-y$ clata $($mole fraction$)$ are available.

$(10$ nils$)$

$\backslash$table$[[x,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8,0\mathrm{.}9,1\mathrm{.}0],[\frac{?}{\text{b}\text{a}\text{r}}(r),0\mathrm{.}23,0\mathrm{.}38,0\mathrm{.}50,0\mathrm{.}62,0\mathrm{.}70,0\mathrm{.}78,0\mathrm{.}86,0\mathrm{.}92,0\mathrm{.}97,1\mathrm{.}0]]$