The feed to a two$-$column fractionation system is $30,000lb\frac{m}{h}$ of a mixture containing $50\%$ benzene $($B$),30\%$ toluene $($T$),$ and $20\%$ xylene $($X$).$ The feed is introduced into column I and results in an overload consisting of $95\%$ benzene, $3\%$ toluene, and $2\%$ xylene. The bottoms from column I are fed to a second column, resulting in an overhead from column II containing $3\%$ benzene, $95\%$ toluene, and $2\%$ xylene. Assume that $52\%$ of the feed appears as overhead in the first column and that $75\%$ of the benzene fed to the second column appears as overhead. Determine the composition and flow rates of all streams not assigned.

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A

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$4$

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${?}^{{?}^{?}}$

$6$

$8$