Oilseeds containing $20\%$ oil by weight will be extracted with pure solvent in a multi$-$stage leaching system. In the extract phase $($overflow$,V_1)$ containing $50\%$ oil by weight, $90\%$ of the oil in the feed will be recovered. Since it is known that $2kg$ of inert solid is carried per $1kg$ of solution in the underflow $(L_N),$ for this solidliquid extraction process calculate;

a$)$ Extract phase $($overflow$)$ flow rate

b$)$ Underflow flow rate and composition

c$)$ The flow rate of solvent used

d$)$ Number of theoretical plates

e$)$ Percentage of non$-$recovered oil