By how much is 30% of 80 greater than 20% of 50?

Concept: A percentage is a rate applied to a base — x% of N means (x/100) × N. When two percentage amounts are built on different bases, they must be evaluated separately and only then compared; the rates themselves cannot be subtracted, because 30% and 20% here act on different quantities (80 and 50).

Application: Convert each percentage into an actual amount, then take the excess of the first over the second.

1. 30% of 80 = (30/100) × 80 = 24

2. 20% of 50 = (20/100) × 50 = 10

3. Excess of the first amount over the second = 24 − 10 = 14

Cross-check: Two independent verifications, plus the contrast that shows why the bases matter.

• Adding back: 10 + 14 = 24, which is exactly 30% of 80, so the subtraction is consistent.

• Benchmark method: 10% of 80 = 8, so 30% of 80 = 3 × 8 = 24; 10% of 50 = 5, so 20% of 50 = 2 × 5 = 10; the gap between them is 14.

• Contrast: subtracting the rates first (30% − 20% = 10%) and applying 10% to 80 or to 50 would give 8 or 5 — neither is the required excess, confirming that each percentage must be evaluated on its own base.

Hence 30% of 80 exceeds 20% of 50 by 14.