$1.900$ kg of crushed oil seeds $(22\%$ oil, $78\%$ meal$)$ is extracted in a three$-$stage cross$-$current unit using $600$ kg of pure hexane in each stage. Determine the fraction of oil extracted using triangular diagram. The equilibrium data are as follows:

Overflow $(100$ kg$)$ solution Underflow $(100$ kg$)$ slurry

WA $($kg$)$ WB $($kg$)$ WC $($kg$)$ W$$A $($kg$)$ W$$B $($kg$)$ W$$C $($kg$)$

$0\mathrm{.}399\mathrm{.}7067\mathrm{.}232\mathrm{.}80$

$0\mathrm{.}4590\mathrm{.}68\mathrm{.}9567\mathrm{.}129\mathrm{.}942\mathrm{.}96$

$0\mathrm{.}5484\mathrm{.}5414\mathrm{.}9266\mathrm{.}9328\mathrm{.}114\mathrm{.}96$

$0\mathrm{.}7074\mathrm{.}4724\mathrm{.}8366\mathrm{.}5825\mathrm{.}068\mathrm{.}36$

$0\mathrm{.}7769\mathrm{.}4629\mathrm{.}7766\mathrm{.}2623\mathrm{.}6210\mathrm{.}12$

$0\mathrm{.}9160\mathrm{.}4438\mathrm{.}6565\mathrm{.}7520\mathrm{.}913\mathrm{.}35$

$0\mathrm{.}9954\mathrm{.}4544\mathrm{.}5665\mathrm{.}3319\mathrm{.}0715\mathrm{.}6$

$1\mathrm{.}1944\mathrm{.}4654\mathrm{.}3564\mathrm{.}3916\mathrm{.}0219\mathrm{.}59$

$1\mathrm{.}2838\mathrm{.}5060\mathrm{.}2263\mathrm{.}7714\mathrm{.}1322\mathrm{.}10$

$1\mathrm{.}2834\mathrm{.}5564\mathrm{.}1763\mathrm{.}2312\mathrm{.}8723\mathrm{.}90$

$1\mathrm{.}4824\mathrm{.}6373\mathrm{.}8961\mathrm{.}549\mathrm{.}6128\mathrm{.}85$

Calculate the fraction of oil extracted in a single stage contactor for the same volume $(1800$kg$)$ of the solvent as mentioned in Question $1$ and comment on the result. Solve using Ponchon$-$Savarit method.