Let ratio of length be a
Let ratio of radii be b
Let ratio of Young's modulus be c
We know $y=\large\frac{F/A}{\Delta L/L}$
$\therefore \Delta L= \large \frac{FL}{AY}$
$\large\frac{\Delta Ls}{\Delta _B}=\bigg(\large\frac{F_S}{F_B}\bigg)\bigg(\large\frac{L_S}{L_B}\bigg)\bigg(\large\frac{A_B}{A_S}\bigg)\bigg(\large\frac{Y_B}{Y_S}\bigg)$
$\qquad= \bigg(\large\frac{3M}{2M}\bigg)$$(a) \bigg(\large\frac{1}{b^2}\bigg)\bigg(\large\frac{1}{c}\bigg)$
$\qquad=\large\frac{3a}{2b^2c}$
$\qquad=\large\frac{3 \times 2}{2 \times 4^2 \times 1}$
$\qquad=\large\frac{3}{16}$
Hence b is the correct answer.