n HDA process a column separating H$\_\{2\}$C$*$H$\_\{4\}$from Benzene. Column feed is $400$mol$/$hr and mole fraction X H$2=0\mathrm{.}0055$X CH$4=0\mathrm{.}0324$; X Bmx $-0\mathrm{.}961$; X Tol $=0$; Assume $99\mathrm{.}85\%$recovery of benzene from feed at the bottom of the column and $100\%$ recovery of H$\_\{2\}$and CH$4$at column overhead. M&S index $800.$Estimate the column overhead vapor distillate flow $($D$),$Liquid flow $($L$)$and vapor $($yi$),$liquid $($xi$)$ composition if the value of equilibrium K H$2=550$; K CH$4=240$and K Benz $=0\mathrm{.}04.$