For the $Pb-Sn$ alloy system,

$($a$)$ What is the compositions and relative amounts of the phases that constitute the eutectic microstructure?

$($b$)$ For an alloy containing $30\%Sn,$

$($i$)$ What are the relative amounts of $$ and $$ phases present at the eutectic temperature?

$($ii$)$ What are the relative amounts of the eutectic and the proeutectic $$ phase present at the same temperature?