$g=\frac{GM}{R^2}$

$M=\rho X V$, where $\rho$ is the density and $V$ is the volume.

$g=\frac{G{\displaystyle \frac{4}{3}}{\mathrm{\pi R}}^3\mathrm{\rho }}{R^2}$

 $g=\frac{4}{3}\pi G\rho R$ 

Given that for first planet

$g_1=\frac{4}{3}\pi {\rho }_{1}G{R}_1$

Second planet

$g_2=\frac{4}{3}\pi {\rho }_{2}G{R}_2$

And $g_1=g_2$

$\Rightarrow \frac{4}{3}\pi {\rho }_{1}G{R}_1=\frac{4}{3}\pi {\rho }_{2}G{R}_2$

$\Rightarrow {\rho }_1{R}_1={\rho }_2{R}_2$

$\frac{{\rho }_1}{{\rho }_2}=\frac{R_2}{R_1}$