A $50$ per cent solution of solute $C$ in solvent $A$ is extracted with a second solvent $B$ in a counter$-$current multiple contact extraction unit. The mass of $B$ is $25$ per cent that of the feed solution, and the equilibrium data are as given in the following figure:

Determine the number of ideal stages required and the mass and concentration of the first extract if the final raffinate contains $15$ per cent of solute $C.$