A batch distillation column with eight theoretical stages $($first stage is the still pot$)$ is charged with $500$ kmol of a $48\mathrm{.}8$ mol$\%$ A in B mixture at atmospheric pressure $($relative volatility $\backslash$alpha AB $=2\mathrm{.}0).$ The boil$-$up rate is constant at $213\mathrm{.}5$ kmol$/$h$.$ If the distillate composition is to be maintained constant at $95$ mol$\%$ A by varying the reflux ratio, calculate the distillation time required to reduce the still composition to $19\mathrm{.}2$ mol$\%$ A$.$ Calculate the fractional recovery of A in the distillate.