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

A$)$ Calculate the composition and amount of the overflow and underflow.

B$)$ Calculate the percentage of sugar extracted from sugar beet.