A liquid mixture consisting of phenol, o$-$cresol, m$-$cresol, and xylene is fractional to give a top product of $95\mathrm{.}3$mol$\%$

phenol. The composition of the top and bottom streams are given below

The mole fraction of xylene in the bottom is

Given:

$a_0=1\mathrm{.}25,a_0=1\mathrm{.}0,a_{20}=0\mathrm{.}63,$ and ${}_{20}=0\mathrm{.}37$