$$2.75\rho$$

Explanation:

The volume of the combined world is:

$$V=\frac{4}{3}\pi\left(\frac{3}{4}R\right)^3=\frac{27}{64}\pi R^3$$

The mass of the combined world is:

$$M=2M$$

The average density of the combined world is:

$$\rho=\frac{M}{V}=\frac{2M}{\frac{27}{64}\pi R^3}=\frac{128}{27}\frac{M}{\pi R^3}=\frac{128}{27}\rho$$

$$=2.75\rho$$