Explanation

(c) Given, $l_{1} = 1K,\ l_{2} = 3K,l_{3} = 5K$
or ${\ \ \ \ m}_{1} = 5m,m_{2} = 3m,m_{3} = 1m$
We knows
$R = \frac{\rho l}{A}$
So $R_{1}:R_{2}:R_{3} = \frac{l_{1}}{A_{1}}\ :\frac{l_{2}}{A_{2}}\ :\frac{l_{3}}{A_{3}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{l_{1}^{2}}{V_{1}}\ :\frac{l_{2}^{2}}{V_{2}}\ :\frac{l_{3}^{2}}{V_{3}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{l_{1}^{2}}{m_{1}}\ :\frac{l_{2}^{2}}{m_{2}}\ :\frac{l_{3}^{2}}{m_{3}}$
$\ \ \ \ \ \ \ \ \ \ = \frac{1}{5}\ :\frac{9}{3}\ :\frac{25}{1} = 1\ :15\ :125$