Two lamps rated 25 W - 220 V and 100 W - 220 V are connected to 220 V supply. Calculate the powers consumed by the lamps.

Given, 

First lamp = 25 W - 220 V 

Second lamp = 100 W - 220 V 

Voltage (V) = 220 V 

Power Consumed (P) = ?

Now, to calculate the resistance

For first lamp,   $P_1 = 25\;W$ 

Voltage $(V_1) = 220\;V$ 

$R_1 = $$ \frac{V_1^{2}}{P_1} = \frac{220^2}{25}$$ = 1936\; \Omega$                                                   [∵ $P = \frac{V^2}{R}$]

For second lamp,   $P_2 = 100\;W$ 

Voltage $(V_2) = 220\;V$ 

$R_2 = $$\frac{V_2^{2}}{P_2} = \frac{220^2}{100}$$ = 484 \; \Omega$ 

If two lamps are connected in series and joined to 220 V mains, then the current  in the circuit (I) is calculated as,

$I = $$\frac{V}{R_1 + R_2} = \frac{220}{1936 + 484}$$ = 0.091 \;A$

Finally, 

Power consumed by the first lamp = $I^2*R_1 = (0.091)^2 * 1936 = 16\;W$ 

Power consumed by the second lamp = $I^2*R_2 = (0.091)^2 * 484 = 4\;W$