For conducting sphere, $\mathrm{V}=\frac{\sigma \mathrm{r}}{\varepsilon_0}$ After contact, $\mathrm{V}_1=\mathrm{V}_2$ $$ \begin{aligned} & \sigma_1 \mathrm{r}_1=\sigma_2 \mathrm{r}_2 \\ & \frac{\sigma_1}{\sigma_2}=\frac{\mathrm{r}_2}{\mathrm{r}_1} \\ & \frac{\sigma_1}{\sigma_2}=3 \end{aligned} $$