Sumit does 600 J of work in 10 min and Amit does 300 J of work in 20 min. Calculate the ratio of the powers delivered by them.

Given: Sumit does 600 J in 10 min; Amit does 300 J in 20 min.

Convert the times to seconds: Sumit: 10 min = 600 s Amit: 20 min = 1200 s

Power = work done ÷ time taken

P_Sumit = 600 ÷ 600 = 1 W P_Amit = 300 ÷ 1200 = 0.25 W

Ratio: P_Sumit : P_Amit = 1 : 0.25 = 4 : 1

Ratio of the powers = 4 : 1

Power is work per unit TIME, so the person who does more work in less time wins twice over. Sumit does double the work in half the time, which is why the ratio is 4 : 1 and not 2 : 1.

Comparing only the work done, 600 : 300, gives 2 : 1 and ignores the time entirely — that is the mistake the question is built to catch.

Because it is a ratio, you could leave both times in minutes and still get 4 : 1, as the units cancel. But convert to seconds if you want the individual powers in watts.