Explanation

(c) Let $\mathcal{Q}$ and q be the charges on the spheres. The potential at the common centre will be
$V = \frac{1}{4\pi\varepsilon_{0}}\left( \frac{\mathcal{Q}}{R} \right) + \frac{1}{4\pi\varepsilon_{0}}\left( \frac{q}{r} \right)$
$= \frac{1}{\varepsilon_{0}}\left\lbrack \frac{\mathcal{Q}}{4\pi R^{2}} \times R + \frac{q}{4\pi r^{2}} \times r \right\rbrack$
But
$\frac{\mathcal{Q}}{4\pi R^{2}} = \frac{q}{4\pi r^{2}} = \sigma$
$\therefore V = \frac{1}{\varepsilon_{0}}\lbrack\sigma R + \sigma r\rbrack = \frac{\sigma}{\varepsilon_{0}}(R + r)$