Explanation

(b) The resistance of one wire
$R_{1} = \rho\frac{l_{1}}{A_{1}}$
and the resistance of second wire
$R_{2} = \rho\frac{l_{2}}{A_{2}}$
Ratio of their resistance
$\frac{R_{1}}{R_{2}} = \frac{l_{1}}{A_{1}} \times \frac{A_{2}}{l_{2}}$
$\because$Mass=density$\times$volume
∵Mass=density ×area ×length
Or $\frac{R_{1}}{R_{2}} = \left( \frac{l_{1}}{l_{2}} \right)^{2} \times \frac{\ _{\rho}A_{2}l_{2}}{\ _{\rho}A_{1}l_{1}}$
Or $\frac{R_{1}}{R_{2}} = \left( \frac{l_{1}}{l_{2}} \right)^{2} \times \frac{m_{2}}{m_{1}}$
Or $\frac{R_{1}}{R_{2}} = \frac{9}{16} \times \frac{3}{2}or\frac{R_{1}}{R_{2}} = \frac{27}{32}$
$\ \ \ \ R_{1}:R_{2} = 27:32\ $