The formula for drift velocity is:
${\mathit{V}}_{\mathit{d}}=\frac{\mathit{I}}{\mathit{n}\mathit{A}\mathit{q}}$
Where A is the cross-sectional area. Since conductors are made of the same material, n and q are constant.
Given:
• Lengths $:{\mathit{l}}_{\mathit{A}}:{\mathit{l}}_{\mathit{B}}=1:2$
• Radii $:{\mathit{r}}_{\mathit{A}}:{\mathit{r}}_{\mathit{B}}=2:3$
$\mathit{R}=\frac{\mathit{\rho }\mathit{l}}{\mathit{A}}$ ⇒ $\mathit{I}=\frac{\mathit{V}\mathit{A}}{\mathit{\rho }\mathit{l}}$
⇒ $\frac{\mathit{V}\mathit{A}}{\mathit{\rho }\mathit{l}}=\mathit{n}\mathit{e}\mathit{A}{\mathit{v}}_{\mathit{d}}$ ⇒ ${\mathit{V}}_{\mathit{d}}=\frac{\mathit{V}}{\mathit{n}\mathit{e}\mathit{\rho }\mathit{l}}$
Here voltage v and n, e, ρ are all same for both conductor so, ${\mathit{V}}_{\mathit{d}}\propto \frac{1}{\mathit{l}}\Rightarrow \frac{{\mathit{V}}_{\mathit{A}}}{{\mathit{V}}_{\mathit{B}}}=\frac{2}{1}$