Percent Change Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Percent Change.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Percent change measures how much a quantity has increased or decreased relative to its original value, calculated as new−originaloriginal×100%\frac{\text{new} - \text{original}}{\text{original}} \times 100\%.

If a price goes from $50 to $60, the change is $10. Compared to the original $50, that's 1050=20%\frac{10}{50} = 20\% increase.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Percent change measures how much something grew or shrank relative to where it started.

Common stuck point: The procedure for percent change is the easy part; the trap is dividing by the new value instead of the original. Asking "Is a change being compared to the original starting value?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is a change being compared to the original starting value?

Worked Examples

Example 1

easy
A jacket originally costs $60\$60 and is on sale for $45\$45. What is the percent decrease?

Answer

25% decrease25\% \text{ decrease}

First step

1
Find the change: 60−45=1560 - 45 = 15.

Full solution

  1. 2
    Divide by the original value: 1560=0.25\frac{15}{60} = 0.25.
  2. 3
    Convert to a percentage: 0.25×100=25%0.25 \times 100 = 25\%.
Percent change is calculated as changeoriginal×100%\frac{\text{change}}{\text{original}} \times 100\%. A decrease means the new value is less than the original.

Example 2

medium
A town's population grew from 12,00012{,}000 to 15,00015{,}000. What is the percent increase?

Example 3

hard
A stock price rises by 20%20\% one year and falls by 20%20\% the next year. If it started at $100\$100, what is the final price and the overall percent change?

Example 4

medium
After a 30%30\% increase, a price becomes $65\$65. What was the original price?

Example 5

medium
A population grew from 5,0005{,}000 to 8,5008{,}500. What is the percent increase?

Example 6

medium
A class had 2020 students; now it has 2424. Express the change as a percent.

Example 7

medium
Sales tax is 8%8\%. The total paid is $54\$54. What was the price before tax?

Example 8

hard
A price increases by 10%10\% in January, then by another 20%20\% in February. What is the overall percent increase?

Example 9

hard
A store advertises 'buy one, get one 50%50\% off.' What is the effective percent discount on the pair?

Example 10

hard
After a 25%25\% increase followed by a discount that returned the price to its original value, what was the discount percent?

Example 11

challenge
A company's revenue increased 25%25\% in Year 1, decreased 20%20\% in Year 2, and increased 40%40\% in Year 3. What is the overall percent change?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A shirt's price increases from $25\$25 to $30\$30. What is the percent increase?

Example 2

medium
After a 15%15\% discount, a laptop costs $680\$680. What was the original price?

Example 3

easy
A price rises from 50to50 to 60. What is the percent change?

Example 4

easy
A value drops from 80to80 to 60. What is the percent change?

Example 5

easy
A quantity goes from 40 to 50. By what percent did it increase?

Example 6

easy
A shirt's price changes from 20to20 to 20. What is the percent change?

Example 7

easy
A population rises from 200 to 240. What is the percent increase?

Example 8

easy
A test score falls from 25 to 20 points. What is the percent decrease?

Example 9

easy
A 40itemismarkedupby40 item is marked up by 10. What percent markup is that?

Example 10

easy
A balance grows from 100to100 to 110. What is the percent change?

Example 11

medium
A $80\$80 jacket is on sale for $68\$68. What is the percent discount?

Example 12

medium
A stock rises 20% from \$50, then the next day the new price falls 20%. What is the final price?

Example 13

medium
A quantity increased by 50% to become 90. What was the original value?

Example 14

medium
A salary goes from $40000\$40000 to $46000\$46000. What is the percent increase?

Example 15

medium
After a 25% discount, a coat costs $60\$60. What was the original price?

Example 16

medium
A number changes from 120 to 150. What is the percent change?

Example 17

challenge
A town's population grows 10% one year and 20% the next. What is the total percent change over two years?

Example 18

challenge
An item's price increased by 25%. By what percent must the new price decrease to return to the original?

Example 19

challenge
A coat costs $120\$120 after a 20% markup on cost. The store then offers 10% off the marked price. What does a customer pay?

Example 20

medium
A $25\$25 book rises to $30\$30. What is the percent increase?

Example 21

medium
A gadget falls from $120\$120 to $90\$90. What is the percent decrease?

Example 22

medium
A quantity grows from 60 to 72. What is the percent increase?

Example 23

easy
A book's price rises from $10\$10 to $12\$12. What is the percent change?

Example 24

easy
A car's price drops from $25,000\$25{,}000 to $20,000\$20{,}000. What is the percent decrease?

Example 25

easy
A bag once held 8080 candies; now it has 100100. What is the percent increase?

Example 26

easy
A test score drops from 9090 to 7272. What is the percent decrease?

Example 27

easy
A salary rises from $60,000\$60{,}000 to $63,000\$63{,}000. What is the percent increase?

Example 28

medium
After a 40%40\% discount, an item costs $36\$36. What was the original price?

Example 29

medium
A price increases by 25%25\% and then decreases by 25%25\%. If the original was $80\$80, what is the final price?

Example 30

medium
A laptop is on sale for $680\$680 after a 15%15\% discount. What was the original price?

Example 31

medium
A jacket is marked up by 20%20\%, then put on a 20%20\%-off sale. If the original cost to the store was $50\$50, what is the final selling price?

Example 32

hard
After three consecutive 10%10\% annual raises, a salary becomes $66,550\$66{,}550. What was the starting salary?

Example 33

hard
A shirt was $60\$60 last year. After two consecutive 20%20\% price increases, what is the new price?

Example 34

hard
A population grows by 5%5\% per year. After how many full years will it exceed double its original size? (Use approximation.)
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Background Knowledge

These ideas may be useful before you work through the harder examples.

percentagessubtractiondivision