$1200$ kg$/$hr of a liquid mixture containing $20\%$ solute, $80\%$ diluent by weight is to be treated in a multistage, countercurrent extraction system. Fresh solvent entering the last stage contains $0\mathrm{.}8\%$ solute by weight. It was found that the same recovery of solute by weight was attained if $5$ stages were present using pure solvent rate which is $1\mathrm{.}5$ times the minimum, and also $3$ stages were present but using a solvent rate which is $2\mathrm{.}2318$ times the minimum. Assume that the solvent and diluent are immiscible and that the equilibrium relation Y $=$ KD X$,$ where X is in kg solute$/$kg diluent and Y is in kg solute$/$kg pure solvent.

Determine:

a$.$ Kd

b$.$Percent recovery of the solute attained

C$.$ Fresh solvent rate requirement for the two cases, kg$/$hr$.$

d$.$ Final extract and raffinate rates for the two cases, kg$/$hr