For Ar, degree of freedom, $f=3$

The specific heat of the mixture at constant pressure is,

$C_{\text {Pmix}}=\frac{n_{1} C_{P 1}+n_{2} C_{P 2}}{n_{1}+n_{2}}$

$=\frac{\frac{1}{4} \times \frac{7}{2} R+\frac{1}{2} \times \frac{5}{8} R}{\frac{1}{4}+\frac{1}{2}}$

$=\frac{17 R}{6}$

The specific heat of the mixture at constant volume is,

$C_{V_{\operatorname{mix}}}=\frac{n_{1} C_{V_{1}}+n_{2} C_{V_{2}}}{n_{1}+n_{2}}$

$=\frac{\frac{1}{4} \times \frac{5}{2} R+\frac{1}{2} \times \frac{3}{8} R}{\frac{1}{4}+\frac{1}{2}}$

$=\frac{11 R}{6}$

The ratio $C_{p} / C_{V}$ of the mixture is,

$\left(\frac{C_{P}}{C_{V}}\right)_{\operatorname{mix}}=\frac{17}{11}$