Bulb $B_1$ is a 50 W bulb working on 100 V and Bulb $B_2$ is a 200 W bulb also working on 100 V. The ratio of resistances of bulbs $B_1$ to $B_2$ is:

4 : 1

The correct answer is Option (1) → 4 : 1

Bulb B1 → 50 W, 100 V
Bulb B2 → 200 W, 100 V

Use the relation:

P = V² / R

So,

R = V² / P

For bulb B1:

R1 = 100² / 50
R1 = 10000 / 50
R1 = 200 ohm

For bulb B2:

R2 = 100² / 200
R2 = 10000 / 200
R2 = 50 ohm

Now,

R1 : R2 = 200 : 50
R1 : R2 = 4 : 1