Questions: Percent Increase and Decrease

Question 1

A jacket originally costs $80 and is now on sale for $60. What is the percent decrease?

• A. 20%
• B. 25%
• C. 33%
• D. 75%

Answer: (B)

Percent decrease = (change ÷ original) × 100 = (20 ÷ 80) × 100 = 25%. The change is $20 and the original (denominator) is $80. A common error is dividing by the new price ($60), which gives approximately 33% — but that uses the wrong base.

Question 2

A store increases prices by 20%, then offers a 20% discount. The final price equals the original price.

• T. True
• F. False

Answer: False

The 20% discount applies to the already-increased price, not the original. Multiplier: 1.20 × 0.80 = 0.96, so the final price is 96% of the original — a 4% net decrease. Each percent change uses the current amount as its base, which is why successive percent changes are multiplicative, not additive.

Question 3

A population grows from 4,000 to 5,200. What is the percent increase? Then, using the multiplier method, find the population after a further 15% increase.

Model answer: 30% increase (1,200 ÷ 4,000 × 100). After a further 15%: 5,200 × 1.15 = 5,980.

The multiplier method converts percent change to a factor: a 15% increase means multiply by 1.15 rather than computing 15% of 5,200 separately and adding. This is more efficient and generalizes directly to compound growth problems, where you chain multipliers together.