The ratio of vapour densities of two gases at the same temperature is $$\frac{4}{25}$$, then the ratio of r.m.s. velocities will be :

We need to find the ratio of rms velocities given the ratio of vapour densities is $$\frac{4}{25}$$.

The root-mean-square velocity of a gas is given by $$v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$$, where $$R$$ is the gas constant, $$T$$ is absolute temperature, and $$M$$ is molar mass.

Vapour density (VD) is defined as the ratio of the mass of a volume of gas to the mass of the same volume of hydrogen under identical conditions, and it is related to the molar mass by $$\text{Vapour Density} = \frac{M}{2}$$. Therefore, the ratio of vapour densities equals the ratio of molar masses: $$\frac{VD_1}{VD_2} = \frac{M_1/2}{M_2/2} = \frac{M_1}{M_2} = \frac{4}{25}$$.

Since at the same temperature $$v_{\text{rms}}\propto\frac{1}{\sqrt{M}}$$, it follows that $$\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{25}{4}} = \frac{5}{2}$$.

The correct answer is Option C: $$\frac{5}{2}$$.