An equimolar feed of propane, butane, pentane, and hexane is to be separated. In the $1^{st}$ column, $95\%$ of propane is to be recovered. The distillate should not contain more than $5\%$ of butane in the feed stream. The feed temperature is $50C.$ Calculate the minimum number of stages.

$\backslash$table$[[$Component$,$Propane,Butane,Pentane,Hexane$],[P_T=50C^{\text{s}\text{a}\text{t}}(mmHg),12493\mathrm{.}2,3693\mathrm{.}48,1194\mathrm{.}2,402\mathrm{.}4]]$