b
For \(A _{2} X\)

\(A _{2} X \rightarrow 2 A ^{+}+ X ^{2-}\)

\(2 S _{1} \quad S _{1}\)

\(K _{ sp }=4 S _{1}^{3}=4 \times 10^{-12}\)

\(S _{1}=10^{-4}\)

for \(MX\)

\(MX \rightarrow M ^{+}+ X ^{-}\)

\(\begin{array}{ll} S _{2}  S _{2}\end{array}\)

\(K _{ sp }= S _{2}^{2}=4 \times 10^{-12}\)

\(S _{2}=2 \times 10^{-6}\)

so \(\frac{ S _{ A _{2} x }}{ S _{ MX }}=\frac{10^{-4}}{2 \times 10^{-6}}=50\)