1. Find the resistance of the lamp in working condition (hot filament).

For a lamp rated $100\text{ W}$ at $200\text{ V}$,

$P = \frac{V^2}{R_{\text{hot}}}$

So,

$R_{\text{hot}} = \frac{V^2}{P} = \frac{(200)^2}{100} = \frac{40000}{100} = 400\,\Omega$

2. Use the given relation between hot and cold resistance.

The hot resistance is about $10$ times the cold resistance:

$R_{\text{hot}} = 10R_{\text{cold}}$

Hence,

$R_{\text{cold}} = \frac{R_{\text{hot}}}{10} = \frac{400}{10} = 40\,\Omega$

3. Match with the options.

$R_{\text{cold}} = 40\,\Omega$

So the correct option is B.