Introduction:
An electric bulb rated at 220V and 100W is designed to operate at a specific voltage and power. However, if the voltage supplied to the bulb is not the same as the rated voltage, the power consumed by the bulb will change.

Formula:
The power consumed by an electric bulb is given by the formula:
Power = (Voltage)² / Resistance

Calculations:
Using the formula, we can calculate the resistance of the bulb at its rated voltage:
Resistance = (Voltage)² / Power
Resistance = (220)² / 100
Resistance = 484 ohms

Case A:
When the bulb is operated on 110V, the power consumed by the bulb will be:
Power = (Voltage)² / Resistance
Power = (110)² / 484
Power = 25W
Therefore, the power consumed by the bulb when operated on 110V is 25W.

Case B:
If the power consumed by the bulb when operated on 110V is 50W, we can use the formula to calculate the resistance of the bulb at this voltage:
Resistance = (Voltage)² / Power
Resistance = (110)² / 50
Resistance = 242 ohms
Now, using the resistance value, we can calculate the power consumed by the bulb at its rated voltage:
Power = (Voltage)² / Resistance
Power = (220)² / 242
Power = 200W
Therefore, the power consumed by the bulb at its rated voltage is 200W.

Conclusion:
In conclusion, the power consumed by an electric bulb is directly proportional to the voltage and inversely proportional to the resistance. If the voltage supplied to the bulb is changed, the power consumed by the bulb will also change.