Percent Problems: 5 Traps to Avoid

Percent questions look easy until the starting number changes mid-problem. These five traps show the wrong answer next to the right one so you can spot the pattern.

1. Stacked discounts are not additive

20% off, then 10% off isn't 30% off. $100 becomes $80, then $72. That's 28% off in total.

2. +20% then −20% is not zero

$100 becomes $120, then $96. You're down 4%, not back to the start.

Why: the second 20% applies to the new amount. 20% of 120 is 24, and 120 − 24 = 96.

3. Percent vs percentage points

Going from 10% to 12% is +2 percentage points, but it's a 20% relative rise (2 is 20% of 10).

4. Average speed is not the average of the speeds

60 mph there and 40 mph back averages 48 mph, not 50, because you spend longer at the slower speed.

For equal distances, average speed = 2ab ÷ (a + b). With a = 60 and b = 40: 2 × 60 × 40 ÷ 100 = 48.

5. Percent of vs percent change

80 to 100 is +25%, but 100 back to 80 is −20%. The starting number changes, so the percentages are not mirrors.

Formula: percent change = (new − old) ÷ old × 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%. From 100 to 80: (80 − 100) ÷ 100 × 100 = −20%.

Everyday checks

• Tip. 20% of $62 is 62 × 0.20 = $12.40. Total $74.40. Common wrong answer: $74, from rounding the tip too early.
• Discount. $85 at 30% off is 85 × 0.70 = $59.50. Common wrong answer: $55, from taking $30 off instead of 30%.
• Growth. $1,000 at 5% a year for 10 years is 1,000 × 1.05^10 = $1,628.89. Common wrong answer: $1,500, from adding 5% ten times instead of compounding.

CalcSolver percent key reminder

On the scientific calculator, 200 + 15% gives 200.15 because 15% becomes 0.15. For 15% more than 200, type 200 × 1.15 to get 230. Use the Percent Calculator when you want percent of, percent change, or the original amount with steps.