Nicotine $($C$)$ in a water $($A$)$ solution containing $5\%$ nicotine is to be extracted with kerosene $(B)$ at $20C.$ Water and kerosene are essentially insoluble. Determine the percentage extraction of nicotine if $100kg$ of feed solution is extracted with three theoretical stages using $50kg$ pure solvent in each stage. Equilibrium relation is given as $y^{\text{'}\text{'}}=0\mathrm{.}923x^{\text{'}},$ where $y^{\text{'}**}$ is the equilibrium value of $kg$ nicotine $\frac{?}{kg}$ kerosene, and $x^{\text{'}}$ is the corresponding value of $kg$ nicotine $\frac{?}{kg}$ water.