Efficiency as useful output over total input

Steps:

• Total energy input rate to device is X.
• Wasted energy rate is Y.
• Useful work rate produced is X - Y.
• Efficiency = useful work rate / total input rate = (X - Y) / X.

Why C is correct:

• Matches definition of efficiency η = (useful output / total input), where total input is X and waste Y subtracts from it.

Why the others are wrong:

• A: X/Y gives total input over waste, which inverts and misapplies the ratio.
• B: (X-Y)/Y gives useful over waste only, ignoring total input.
• D: (X-Y)/(X+Y) incorrectly assumes total input is X + Y instead of X.

Final answer: C