Input power ratio from efficiency for equal output

Steps:

• Efficiency η = useful output / input power, so input power P_in = output / η.
• Both lamps have same output, so P_in_old = output / 0.05 and P_in_new = output / 0.40.
• Ratio P_in_new / P_in_old = (output / 0.40) / (output / 0.05) = 0.05 / 0.40 = 0.125.
• 0.125 rounds to 0.13.

Why A is correct:

• Ratio of input powers equals inverse ratio of efficiencies (η_old / η_new = 5%/40% = 0.125 ≈ 0.13), per efficiency definition.

Why the others are wrong:

• B: 0.63 misapplies ratio as η_new / (η_new + η_old) ≈ 40/63.
• C: 1.6 inverts the ratio, giving η_new / η_old = 40/25 (wrong denominator).
• D: 0.8 confuses with η_new / 100% = 40/50.

Final answer: A