Solution :
$E_1-E_2=1312 \times Z^2 \bigg(\large\frac{1}{1^2}-\frac{1}{2^2}\bigg)$$=1312 \times Z^2\bigg(\large\frac{3}{4}\bigg)$
$E_2-E_3=1312 \times Z^2 \bigg(\large\frac{1}{2^2}-\frac{1}{3^2}\bigg)$
$\qquad= 1312 \times Z^2\bigg(\large\frac{5}{36}\bigg)$
From these equation
$\large\frac{E_1-E_2}{E_2-E_3}=\frac{3 \times 36}{4 \times 5}=\frac{27}{5}$