Consider the Pb$-$Sn phase diagram in Fig. $1.$

a$)$ Locate the point in the phase diagram for a $40wt\%Sn-60wt\%Pb$ alloy at $150C,$ and indicate what phases are present and their compositions?

b$)$ For a$),$ calculate the relative amount of each phase present in terms of mass fraction, using the lever rule.

c$)$ With the aid of sketches, describe in detail the development of the solid microstructure for $40\%Pb-60\%Sn$ on cooling from $300C$ to room temperature, under pseudo$-$equilibrium conditions.