Three concentric spherical metallic shells X ,   Y and Z of radius a ,   b and c respectively a…

The charges on the spheres are

 $$\begin{gathered} q_X=\sigma 4\pi a^2 \\ {q}_Y=-\sigma 4\pi b^2 \\ {q}_Z=\sigma 4\pi c^2 \end{gathered}$$

It is given that $V_X=V_Z$

So, 

$$\begin{gathered} \frac{q_X}{4\pi {\epsilon }_{0}a}+\frac{q_Y}{4\pi {\epsilon }_{0}b}+\frac{{\displaystyle q_Z}}{{\displaystyle 4\pi {\epsilon }_{0}c}}=\frac{{\displaystyle q_X}}{{\displaystyle 4\pi {\epsilon }_{0}c}}+\frac{{\displaystyle q_Y}}{{\displaystyle 4\pi {\epsilon }_{0}c}}+\frac{{\displaystyle q_Z}}{{\displaystyle 4\pi {\epsilon }_{0}c}} \\ \Rightarrow \frac{\sigma 4\pi a^2}{a}-\frac{{\displaystyle \sigma 4\pi b^2}}{{\displaystyle b}}+\frac{{\displaystyle \sigma 4\pi c^2}}{{\displaystyle c}}=\frac{{\displaystyle \sigma 4\pi (a^2-b^2+c^2)}}{{\displaystyle c}} \\ \Rightarrow c(a-b+c)=(a^2-b^2+c^2) \\ \Rightarrow c=a+b=2 \mathrm{cm}+3 \mathrm{cm}=5 \mathrm{cm} \end{gathered}$$