It is proposed to reduce the concentration of acetaldehyde in aqueous solution from $50$ per cent to $5$ per cent by mass, by extraction with solvent $S$ at $293K.$ If a counter$-$current multiple contact process is adopted and $0\mathrm{.}015k\frac{g}{s}$ of the solution is treated with an equal quantity of solvent, determine the number of theoretical stages required and the mass and concentration of the extract from the first stage. The equilibrium relationship for this system at $293K$ is as follows: