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Question

Difficulty: EasyFractions, Decimals, and Percents Arithmetic

The original price of a sweater is $40\$40. If the price is increased by 25%25\%, and then the new price is decreased by 10%10\%, what is the final price of the sweater?

  1. A
    $44\$44
  2. $45\$45Answer
  3. C
    $46\$46
  4. D
    $50\$50
  5. E
    $36\$36

Answer

The final price of the sweater is $45\$45.
Increasing the original price of $40\$40 by 25%25\% yields an intermediate price of $50\$50 (since 25%25\% of $40\$40 is $10\$10). Decreasing $50\$50 by 10%10\% reduces the price by $5\$5 (since 10%10\% of $50\$50 is $5\$5), resulting in a final price of $45\$45.

Step-by-Step Solution

1
Calculate the price after the initial 25%25\% increase.
The price increases by 25%25\% of $40\$40, which is 0.25×$40=$100.25 \times \$40 = \$10. The new intermediate price is $40+$10=$50\$40 + \$10 = \$50.
Percentage increases must be calculated using the starting base value.
2
Calculate the final price after the 10%10\% decrease.
The discount is 10%10\% of the intermediate price of $50\$50, which is 0.10×$50=$50.10 \times \$50 = \$5. Subtracting this from the intermediate price gives $50−$5=$45\$50 - \$5 = \$45.
Successive percentage changes apply to the updated base value, not the original starting value.

Key Concept

Successive Percentage Changes and Base Value Alignment
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Topics

Fractions, Decimals, and Percents Arithmetic

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