A flask contains argon and oxygen in the ratio of 3: 2 in mass and...

Given here, $\dfrac{{m}_{Ar}}{{m}_{O}} = \dfrac{3}{2}$.

As argon is monoatomic gas, so it has three degree of freedom $\left(f\right)$ and oxygen is a diatomic gas, so its degree of freedom is five.

We know that average kinetic energy per molecule is given by $KE = \dfrac{f}{2}kT$, where, $k$ is Boltzmann's constant and $T$ is temperature.

Here, $T = 27 ° C$ is fixed for both gas.

So, $\dfrac{{\left(KE\right)}_{Ar}}{{\left(KE\right)}_{O}} = \dfrac{\dfrac{3}{2}kT}{\dfrac{5}{2}kT} = \dfrac{3}{5}$