A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

$$Q_1 + Q_2 = Q$$

Equal surface charge density condition: $$\sigma_1 = \sigma_2 \implies \frac{Q_1}{4\pi r^2} = \frac{Q_2}{4\pi R^2} \implies \frac{Q_1}{r^2} = \frac{Q_2}{R^2}$$

Charges on each shell: $$Q_1 = \frac{r^2}{R^2 + r^2}Q$$ and $$Q_2 = \frac{R^2}{R^2 + r^2}Q$$

Potential at the common centre: $$V = \frac{1}{4\pi\varepsilon_0}\frac{Q_1}{r} + \frac{1}{4\pi\varepsilon_0}\frac{Q_2}{R}$$

$$V = \frac{1}{4\pi\varepsilon_0}\left[\frac{rQ}{R^2+r^2} + \frac{RQ}{R^2+r^2}\right] = \frac{1}{4\pi\varepsilon_0}\frac{(R+r)}{(R^2+r^2)}Q$$