For $2^{\text {nd }}$ gas $\frac{C_{P_{2}}}{C_{V_{2}}}=\frac{4}{3} \Rightarrow C_{P_{2}}=4 x$ and $C_{V_{2}}=3 x$

Now for mixture $\mathrm{C}_{\mathrm{P}}=\frac{\mathrm{n}_{1} \mathrm{C}_{\mathrm{P}}+\mathrm{n}_{2} \mathrm{C}_{\mathrm{B}_{2}}}{\mathrm{n}_{1}+\mathrm{n}_{2}}=\frac{17 \mathrm{R}}{5}$

$C_{V}=\frac{n_{1} C_{V_{1}}+n_{2} C_{V_{3}}}{n_{1}+n_{2}}=\frac{12 R}{5}$

$\Rightarrow \frac{C_{p}}{C_{v}}=\frac{2(5 x)+3(4 x)}{2(3 x)+3(3 x)}=\frac{17}{12}$

$\Rightarrow \frac{C_{P}}{C_{V}} \approx 1.42$