A 40 watt lamp requires 0.182 A of current at 220 volts, while a 60 watt lamp requires 0.272 A of current at 220 volts. If a 40 watt lamp and a 60 watt lamp are connected in series with a 220 volt line, how many amperes of current will flow through each lamp?

Let the current flowing through the two lamps, which are connected in series, be I.
Let their individual resistances be R₁ and R₂ and their power be P₁ and P₂
Then for the lamp1 R₁ = = 1210 Ω
Similarly for the lamp2  R₂ = = 806.67 Ω
Therefore when they are connected in series the net resistance of the two lamps is the sum of their individual resistances R = R₁ + R₂ = 2016.67 Ω
Therefore the current I = = 0.109 A.