The moment of inertia of the ring about an axis perpendicular to the plane of ring is $I_r=m{k}^2$.

The moment of inertia of the sphere is 

$I_s=\frac{2}{5}m{R^2}_s$

It is given that 

$m{k}^2=m{R^2}_r=\frac{2}{5}m{R_s}^2 ...\left(i\right)$

From equation (i)

$R_r=\sqrt{\frac{2}{5}}{R}_s$

From the question, it can be written that

$\frac{R_r}{R_s}=\sqrt{\frac{2}{x}}$

$$\begin{gathered} \Rightarrow \frac{R_r}{R_s}=\sqrt{\frac{2}{5}} \\ \Rightarrow x=5 \end{gathered}$$