\(\Delta x=\frac{F L}{A Y}\)

For wire \(A\)

\(\Delta L_A=\frac{F \cdot L_A}{\pi r_A^2 \cdot Y_A} \ldots (1)\)

For wire \(B\)

\(\Delta L_B=\frac{F \cdot L_B}{\pi r_B^2 \cdot Y_B} \ldots (2)\)

Divide \((1)\) by \((2)\)

\(\frac{\Delta L_A}{\Delta L_B}=\frac{F \cdot L_A}{\pi r_A^2 \cdot Y_A} \times \frac{\pi r_B^2 \cdot Y_B}{F \times L_B}=\frac{L_A}{L_B} \times\left(\frac{r_B}{r_A}\right)^2 \times \frac{Y_B}{Y_A}\)

Substituting the value of ratio's

\(\frac{\Delta L_A}{\Delta L_B}=\frac{4}{1} \times\left(\frac{1}{3}\right)^2 \times \frac{2}{1}=\frac{8}{9}\)