Let potential drop unit length a potentiometer wire be $\mathrm{K}.$

For zero deflection the current will flow independently in two circles

$\mathrm{IR}=\mathrm{K} \times 10$               ............$(1)$

$\mathrm{IR}+\mathrm{IX}=\mathrm{K} \times 30$          .........$(2)$

$(2)-(1)$

$\Rightarrow \mathrm{IX}-\mathrm{k} \times 20$       ........$(3)$

Divide $(1)$ and $(2)$

$\frac{\mathrm{R}}{\mathrm{X}}=\frac{1}{2} \Rightarrow \mathrm{x}=2 \mathrm{\,R}$