Three concentric spherical metallic shells X, Y and Z of radius a,...

The charges on the spheres are

${q}_{X} = \sigma4\pi{a}^{2}{q}_{Y} = - \sigma4\pi{b}^{2}{q}_{Z} = \sigma4\pi{c}^{2}$

It is given that ${V}_{X} = {V}_{Z}$

So,

$\dfrac{{q}_{X}}{4\pi{ε}_{0}a} + \dfrac{{q}_{Y}}{4\pi{ε}_{0}b} + \dfrac{{q}_{Z}}{4\pi{ε}_{0}c} = \dfrac{{q}_{X}}{4\pi{ε}_{0}c} + \dfrac{{q}_{Y}}{4\pi{ε}_{0}c} + \dfrac{{q}_{Z}}{4\pi{ε}_{0}c} ⇒ \dfrac{\sigma4\pi{a}^{2}}{a} - \dfrac{\sigma4\pi{b}^{2}}{b} + \dfrac{\sigma4\pi{c}^{2}}{c} = \dfrac{\sigma4\pi ( {a}^{2} - {b}^{2} + {c}^{2} )}{c} ⇒ c ( a - b + c ) = ( {a}^{2} - {b}^{2} + {c}^{2} ) ⇒ c = a + b = 2cm + 3cm = 5cm$