Hello Dear.Given :-Ratio of the Resistance of two bulbs P and Q = 1 : 2.Let the Resistance of the bulbs P and Q be x and 2x respectively.∵ Current remains same in the series,∴ Let the current in the Resistors P and Q be I.Now,\xa0For Bulbs P,Power = P₁Current = IResistance = x∵ Power = I² × R∴ P₁ = I²\xa0× xFor Bulb Q,Power = P₂Current = IResistance = 2x∴ Power(P₂) = I²\xa0× 2x∴ Ratio of the Powers,P₁/P₂ = I²x/I²2xP₁/P₂ = 1/2⇒ P₁ : P₂ = 1 : 2Hence, the Ratio between the Power\xa0Dissipation of the bulb P and bulb Q is 1 : 2.Hope it helps.