Question

A number is first increased by 20% and then decreased by 20%. What is the net increase or decreased in the original number?

• A. 20% increase
• B. 10% increase
• C. 4% increase
• D. 4% decrease

Answer 1

Answer:

D. 4% decrease

Percentage Change Calculations

• Understanding the Problem: This type of problem involves successive percentage changes. When a number is increased by a percentage and then decreased by the same percentage, the net result is always a decrease.

• Mathematical Approach: Let the original number be 100.

• Step 1: Increase by 20%

  • A 20% increase on 100 is (20/100) * 100 = 20.

  • The new number becomes 100 + 20 = 120.

• Step 2: Decrease by 20%

  • The decrease is calculated on the *new* number (120), not the original number.

  • A 20% decrease on 120 is (20/100) * 120 = 24.

  • The final number becomes 120 - 24 = 96.

• Calculating Net Change:

  • The original number was 100, and the final number is 96.

  • The net change is 96 - 100 = -4.

  • This represents a decrease of 4%.

• Formula for Successive Percentage Change: For two successive percentage changes of x% and y% (where positive values indicate increase and negative values indicate decrease), the net percentage change is given by: x + y + (xy/100)%.

• Applying the Formula:

  • Here, the first change is +20% and the second change is -20%.

  • Net change = 20 + (-20) + (20 * -20)/100

  • Net change = 0 + (-400)/100

  • Net change = -4%

  • A negative sign indicates a decrease.