Percent Increase and Decrease

Show your work for each problem.

1.
A shirt's price increased from 40 dollars to 50 dollars. What is the percent increase?
1. a)50%
2. b)20%
3. c)25%
4. d)10%
Answer: 25%
Change = 50 - 40 = 10. Percent increase = 10/40 = 0.25 = 25%. Note: 20% would be if you divided by 50 (the new value) - a common mistake!
2.
A laptop's price dropped from 1000 euros to 800 euros. What is the percent decrease?
1. a)200%
2. b)80%
3. c)25%
4. d)20%
Answer: 20%
Change = 200. Percent decrease = 200/1000 = 0.20 = 20%. 25% would be if you divided by 800 (wrong denominator). 80% is what remains, not the decrease.
3.
What multiplier should you use for a 15% increase?
Answer: 1.15
A 15% increase means you keep 100% and add 15%. As a multiplier:
4.
What multiplier should you use for a 30% decrease?
Answer: 0.70
A 30% decrease means you keep 100% - 30% = 70%. As a multiplier:
5.
A book costs 20 euros. After a 25% increase, what is the new price?
Answer: 25
1. What is the multiplier for a 25% increase? 1.25
2. Multiply the original price by the multiplier: 20 × 1.25 = ? 25
6.
A jacket costs 80 dollars. It's on sale for 20% off. What is the sale price?
Answer: 64
1. What is the multiplier for a 20% decrease? 0.80
2. Multiply the original price by the multiplier: 80 × 0.80 = ? 64
7.
A population grew from 250,000 to 300,000. What is the percent increase?
1. a)20%
2. b)25%
3. c)16.7%
4. d)50%
Answer: 20%
Change = 50,000. Percent increase = 50,000/250,000 = 0.20 = 20%. 16.7% would be 50,000/300,000 (wrong denominator).
8.
A salary increased from 2500 euros to 2750 euros. What is the percent increase?
Answer: 10
Percent increase = (2750 - 2500)/2500 × 100 = 250/2500 × 100 = 0.10 × 100 = 10%
9.
A phone costs 600 euros. It's on sale for 15% off. What is the sale price?
Answer: 510
1. What is the multiplier for a 15% decrease? 0.85
2. Calculate the sale price: 600 × 0.85 = ? 510
10.
A restaurant meal costs 45 euros. You add a 20% tip. What is the total?
Answer: 54
1. What is the multiplier for a 20% increase? 1.20
2. Calculate the total: 45 × 1.20 = ? 54
11.
A stock dropped from 80 dollars to 68 dollars. What is the percent decrease?
1. a)12%
2. b)85%
3. c)15%
4. d)17.6%
Answer: 15%
Change = 12. Percent decrease = 12/80 = 0.15 = 15%. 17.6% would be 12/68 (wrong). 85% is what remains, not the decrease.
12.
A price dropped from 90 euros to 72 euros. What is the percent decrease?
Answer: 20
Percent decrease = (90 - 72)/90 × 100 = 18/90 × 100 = 0.20 × 100 = 20%
13.
After a 20% increase, a membership costs 72 euros. What was the original price?
Answer: 60
1. What multiplier was used for the 20% increase? 1.20
2. If Original × 1.20 = 72, then Original = 72 ÷ 1.20 = ? 60
14.
After a 25% discount, a TV costs 450 euros. What was the original price?
Answer: 600
1. What multiplier was used for the 25% discount? 0.75
2. If Original × 0.75 = 450, then Original = 450 ÷ 0.75 = ? 600
15.
A price increases by 50%, then decreases by 50%. What is the net percent change from the original?
1. a)25% increase
2. b)50% decrease
3. c)0% (back to original)
4. d)25% decrease
Answer: 25% decrease
Start with 100. After +50%: 100 × 1.5 = 150. After -50%: 150 × 0.5 = 75. Net change: (75-100)/100 = -25% (25% decrease). The decreases are NOT inverse operations!
16.
A stock went from 60 dollars to 45 dollars to 54 dollars. What is the overall percent change?
Answer: -10
1. What is the overall change from start (60) to end (54)? -6
2. Divide by the original (60): -6/60 = ? -0.10
3. Convert to percent: -0.10 × 100 = ? -10
17.
A shop increases prices by 10%, then offers a 10% sale. If an item originally cost 100 euros, what does it cost now?
Answer: 99
After +10%: 100 × 1.10 = 110. After -10%: 110 × 0.90 = 99€. You don't get back to 100 because the 10% decrease is of a larger number (110).
18.
A company's revenue went from 2 million to 2.4 million euros. What single percent increase is this?
Answer: 20
1. What is the change in revenue? (in millions) 0.4
2. Divide by the original revenue: 0.4/2 = ? 0.20
3. Convert to percent: 0.20 × 100 = ? 20