A 100 W bulb working on 200 V and a 200 W bulb on 100 V, have their resistances in the ratio

8 : 1

The correct answer is Option (2) → 8 : 1

Power formula: $P = \frac{V^2}{R} \;\;\Rightarrow\;\; R = \frac{V^2}{P}$

For 100 W, 200 V bulb:

$R_1 = \frac{200^2}{100} = \frac{40000}{100} = 400 \; \Omega$

For 200 W, 100 V bulb:

$R_2 = \frac{100^2}{200} = \frac{10000}{200} = 50 \; \Omega$

Ratio: $\; R_1 : R_2 = 400 : 50 = 8 : 1$