Explanation

(d) Let $\left( \rho_{A},l_{A},r_{A},A_{A} \right)$ and $(\rho_{B},l_{B},r_{B},A_{B})$are specific resistances, lengths, radii and areas of wires A and B respectively.
Resistance of
$A = R_{A} = \frac{\rho_{A}l_{A}}{A_{A}} = \frac{\rho_{A}l_{A}}{\pi R_{A}^{2}}$
Resistance of
$B = R_{B} = \frac{\rho_{B}l_{B}}{A_{B}} = \frac{\rho_{B}l_{B}}{\pi r_{B}^{2}}$
For given information
$\rho_{B} = 2\rho_{A}$
$r_{B} = 2r_{A}$
And $R_{A} = R_{B}$
$\therefore\ \frac{\rho_{A}l_{A}}{\pi r_{A}^{2}} = \frac{\rho_{B}l_{B}}{\pi r_{B}^{2}}$
$\Longrightarrow \ \frac{\rho_{A}l_{A}}{\pi r_{A}^{2}} = \frac{2\rho_{A} \times l_{B}}{\pi\left( 2r_{A} \right)^{2}}$
$\Longrightarrow \ \ \ \ \ \ \frac{l_{B}}{l_{A}} = \frac{2}{1} = 2:1$