QUESTION $2$: Binary continuous distillation

$(30)$

A distillation column shown in figure $2$ is used to separate acetone from ethanol. The feed contains $40\%$ acetone on a mole basis and has a flow rate of $100mo\frac{l}{h}.$ The saturated vapour feed is fed on the $3^{rd}$ plate from the bottom of the column. The column operates at $1$ atmosphere and contains a total condenser and a partial reboiler with a reflux ratio of $3$ and a boil up ratio of $\frac{5}{6}.$ A liquid side stream of $66\%$ acetone is withdrawn from the column and is sent through an intermediate reboiler and sent back to the column as a saturated vapour. The desired products: $89\%$ acetone in the distillate and $10\%$ acetone in the bottoms.

Marks will be allocated for all the intermediate calculations and method, showing a correct thought process.

Find the number of stages required for the desired separation, and find on which plate the side stream $S_1$ will be withdrawn, and on which plate the second feed stream $S_2$ will be fed.