$(45$ points$)$ A continuous deodorizing system, involving a counter flow steam stripping

operation, is under consideration for the removal of taints from cream. The taint component

is present in the cream to the extent of $13$ parts per million $(ppm)$ and is supposed to be

reduced down to $0\mathrm{.}2ppm$ in the leaving cream. If the relative flow rates of cream and steam

are given in the ratio $1$:$0\mathrm{.}8,$ calculate the concentration of the taint in the leaving cream. The

equilibrium concentration distribution of the taint has been found experimentally to be in the

ratio of $1$ in the cream to $10$ in the steam and it is assumed that equilibrium is reached in each

stage. Calculate how many contact stages would be required assuming $($a$)100\%$ stage

efficiency, and $($b$)70\%$ stage efficiency using both the graphial approach and the analytical

equations?