1. Relation between vapour density and molar mass

   Vapour density (V.D.) is proportional to molar mass: $\text{V.D.} = \frac{M}{2}$ Hence, the ratio of vapour densities is the same as the ratio of molar masses: $\frac{\text{V.D.}_1}{\text{V.D.}_2} = \frac{M_1}{M_2} = \frac{4}{25}$

2. Formula for r.m.s. velocity

   The r.m.s. velocity of a gas is: $v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ At the same temperature, $v_{\text{rms}} \propto \frac{1}{\sqrt{M}}$

3. Find the ratio of r.m.s. velocities

   Therefore, $\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}$ Since $\frac{M_1}{M_2} = \frac{4}{25}$ we get $\frac{M_2}{M_1} = \frac{25}{4}$ So, $\frac{v_1}{v_2} = \sqrt{\frac{25}{4}} = \frac{5}{2}$

4. Option check

   • A: $\frac{5}{2}$ ✅
   • B: $\frac{25}{4}$ ❌
   • C: $\frac{4}{25}$ ❌
   • D: $\frac{2}{5}$ ❌

Therefore, the correct answer is: $\boxed{\frac{5}{2}}$