Percent change shows up in more word problems than almost any other topic: raises, sales, price hikes, population growth, test scores, depreciation, investment returns. Most of these problems are variations on just five patterns, and the mistakes students make are just as predictable. This generator produces a fresh problem in any of the five patterns at three difficulty levels, and every solution names the trap to avoid.
How to use the percent change problem generator
- Choose a problem type — or Mixed for variety.
- Choose a difficulty. Easy problems use friendly percents like 10%, 25% and 50%; medium adds 5%, 8%, 12% and 15%; hard uses rates such as 2.5%, 7.5% and 12.5% plus successive changes.
- Click New problem, solve it on paper, then compare with the worked solution under the answer.
The five patterns
| Pattern | What you know | What you find | Key formula |
|---|---|---|---|
| Find the % increase | Old and new values | Percent | (new − old) ÷ old × 100 |
| Find the % decrease | Old and new values | Percent | (old − new) ÷ old × 100 |
| Apply a change | Original and percent | New value | original × (1 ± p/100) |
| Reverse a change | New value and percent | Original | new ÷ (1 ± p/100) |
| Successive changes | Two percents | Overall percent | (1 ± p₁/100)(1 ± p₂/100) − 1 |
Worked examples
Find the increase: A town grows from 12,500 to 13,750 people. Change = 1,250; 1,250 ÷ 12,500 = 0.10 → 10% increase.
Apply a decrease: An $80 jacket is 25% off. 80 × 0.75 = $60.
Reverse a raise: After a 20% raise, pay is $21.60/hour. 21.60 ÷ 1.20 = $18.00 before the raise.
Successive changes: A stock rises 10%, then falls 10%. 1.10 × 0.90 = 0.99 → 1% lower overall.
The three classic traps
Dividing by the wrong value
Percent change always compares with the original. A price drop from $50 to $40 is $10 ÷ $50 = 20%, not $10 ÷ $40 = 25%. Reading “from … to …” carefully tells you which value is the original.
Undoing a change with the same percent
If a coat is $64 after 20% off, the original is not $64 + 20% of $64 = $76.80. The discount was 20% of the original, so $64 is 80% of it: $64 ÷ 0.8 = $80. The reverse-percentage problems in this generator show the tempting wrong answer next to the right one.
Adding successive percentages
A 30% increase followed by a 30% decrease is not 0%. Multiplying the factors, 1.3 × 0.7 = 0.91, shows a 9% loss. The same logic explains why two 10% raises give 21%, not 20%.
Tips that make every problem easier
- Use multipliers. A 15% increase means “multiply by 1.15”; a 15% decrease means “multiply by 0.85”. Chains of changes become chains of multiplications.
- Estimate. 12.5% of $19.92 is about one eighth of $20, or $2.50 — so an answer near $22.40 makes sense.
- Work in cents for money if decimals cause trouble, and round only the final answer.
- Write a sentence answer: “The rent increased by 15%.”
To check your own numbers rather than generated ones, use the percentage change calculator, or the dedicated percentage increase and percentage decrease calculators. For shopping math with dollar savings, the discount calculator is the practical tool.
Frequently asked questions
How do you solve percent change word problems?
Identify the original value and the new value, subtract to find the change, divide the change by the original value and multiply by 100. If a town grows from 12,500 to 13,750 people, the change is 1,250 and 1,250 ÷ 12,500 × 100 = 10%.
How do I find the original price after a discount?
Divide the sale price by the share that remains. After 20% off, 80% remains, so a $64 sale price came from 64 ÷ 0.80 = $80. Adding 20% of $64 to the sale price would give $76.80, which is wrong.
Why isn't a 20% increase followed by a 20% decrease zero?
The decrease is taken from the larger, increased amount. 100 becomes 120, and 20% of 120 is 24, so it drops to 96 — an overall change of −4%. Multiply the factors: 1.20 × 0.80 = 0.96.
What grade level are percent change problems?
In the Common Core standards, percent increase and decrease appear in grade 7 (7.RP.A.3), alongside markups, markdowns, tax and percent error. The easy setting suits grades 6–7, while successive changes and reverse percentages are good practice for grade 8 and up.
What are some common mistakes in percent word problems?
Dividing by the new value instead of the original, adding percentages from successive changes, and reversing a change by applying the same percentage to the new amount. The worked solutions call out each of these traps.