A feed of $30$mol$\%$ methanol $(A),20\%$ ethanol $($B$),15\%n-$propanol $($C$),$ and $35\%n$ butanol $(D)$ is distilled at $101\mathrm{.}32$kPa abs pressure to give a distillate composition containing $95\mathrm{.}0$ mol $\%$ methanol and residue composition containing $5\mathrm{.}0\%$ methanol and the other containing reflux ratio is $3\mathrm{.}0.$ Assume Raoult's law applies and use vapor$-$pressure data given below.

a$)$ Compositions and amounts of distillate and bottoms for feed of $100mo\frac{l}{h}.$

b$)$ Top $(62-68C)$ and bottom $(92-98C)$ temperatures and number of stages at total reflux.

Vapor Pressures $($atm$)$