\(A_{v}=\beta \times \frac{R_{\text {out }}}{R_{\text {in }}}\)

Transconductance, \(g_{m}=\frac{\beta}{R_{\mathrm{in}}}\) or \(R_{\mathrm{in}}=\frac{\beta}{g_{m}}\)

\(\therefore \quad A_{v}=g_{m} R_{\mathrm{out}}\)

For first case, \(A_{v}=G, g_{m}=0.03\, \mathrm{mho}, \beta=25\)

\(\therefore \quad G=0.03 R_{\text {out }}\)   ........ \((i)\)

For second case, \(A_{v}=G^{\prime}, g_{m}=0.02\, \mathrm{mho}\),\( \beta=20\)

\(\therefore \quad G^{\prime}=0.02\,R_{\text {out }}\)   ........ \((ii)\)

Divide \((ii)\) by \((i)\), we get

\(\frac{G^{\prime}}{G}=\frac{2}{3} \text { or } G^{\prime}=\frac{2}{3}\,G\)