Density and masses of wire are same so their volumes are same i.e. $A_1 I_1 = A_2 I_2$

Ratio of resistances of wires A and $\mathrm{B} \frac{R_A}{R_B}$

$= \frac{l_1}{l_2} \times \frac{A_2}{A_1} = \left(\frac{A_2}{A_1}\right)^2 = \left(\frac{r_2}{r_1}\right)^4$ Since $r_1 = 2r_2$ so $\frac{R_A}{R_B} = \frac{1}{16}$

$\Rightarrow R_{B} = 16 R_{A}$

Resistance RA and RB are connected in parallel so equivalent resistance $R = R_A R_B / R_A + R_B = 16 R_A / 17$ By checking correctness of equivalent resistance from options, only option is correct.