A counter$-$current leaching with water is to be used in order to obtain sugar from $200kg$ of sugar beet. It contains $24\%$ sugar, $14\%$ moisture and $62\%$ inert insoluble solid. It is desired that, the final extract contains $1\mathrm{.}2kg$ sugar$/8kg$ water and slurry should have sugar not exceed $0\mathrm{.}05kg$ sugar$/kg$ inert solid. The value of $N$ for the slurry is constant. Calculate;

a$)$ the composition and amount of the overflow and the underflow

b$)$ the percentage of sugar extracted from sugar beet.