A feed stream $(200$ kg$/$h$)$ containing $40\%$ mass of acetone in water is mixed with a solvent containing $5\%$ water in $95\%$ MIBK in an extractor. The ratio of solvent to feed is $1$:$1.$

Calculate

$($i$)$ The mass fractions of each component $($Acetone$,$ Water and MIBK$)$ in mixed phase $($M$)$ in the mixer, and in Extract $($E$)$ and Raffinate $($R$)$ phase in the settler

$($ii$)$ The flow rates of Extract $($E$)$ and Raffinate $($R$).$

$($iii$)$ Show graphically the mixing point $($M$),$ E and R phase compositions

Please use the following ternary diagram for the calculations.