A mixture of benzene and toluene containing $60$mole$\%$ benzene is to be separated to give a product of $95$mole$\%$ benzene and bottom product containing $10$mole$\%$ benzene. The feed enters a column at its bubble point. It is proposed to operate the column with reflux ratio of $2\mathrm{.}5.$ Calculate number of theoretical plates needed by Mccabe$-$Thiele method and position of feed plate. The vapor liquid equilibrium data are given as below:

$\backslash$table$[[x,0,0\mathrm{.}05,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5],[y,0,0\mathrm{.}13,0\mathrm{.}21,0\mathrm{.}375,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7]]$

$\backslash$table$[[x,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8,0\mathrm{.}9,1\mathrm{.}0],[y,0\mathrm{.}77,0\mathrm{.}83,0\mathrm{.}9,0\mathrm{.}95,1\mathrm{.}0]]$