b
Due to induction net charges on outer surface of spheres are as shown.
$\sigma =\frac{\mathrm{Q}_{1}}{4 \pi \mathrm{R}^{2}}=\frac{\mathrm{Q}_{1}+\mathrm{Q}_{2}}{4 \pi(2 \mathrm{R})^{2}}=\frac{\mathrm{Q}_{1}+\mathrm{Q}_{2}+\mathrm{Q}_{3}}{4 \pi(3 \mathrm{R})^{2}}$
$\Rightarrow \mathrm{Q}_{1}=\frac{\mathrm{Q}_{1}+\mathrm{Q}_{2}}{4}=\frac{\mathrm{Q}_{1}+\mathrm{Q}_{2}+\mathrm{Q}_{3}}{4 \pi(3 \mathrm{R})^{2}}$
$\Rightarrow \mathrm{Q}_{2}=3 \mathrm{Q}_{1}$ and $\mathrm{Q}_{3}=5 \mathrm{Q}_{1}$
$\therefore \mathrm{Q}_{1}: \mathrm{Q}_{2}: \mathrm{Q}_{3}=1: 3: 5$