Question

A number is increased by 20% and then decreased by 20%. What is the overall percentage change?

• A. No change
• B. 4% decrease
• C. 4% increase
• D. 8% decrease

Hint:

Increasing and decreasing a number by the same percentage never gives the original value back. Equal percentage increase and decrease always result in a net decrease.

Answer 1

The Correct Option is B

Concept: Successive percentage increase and decrease are not directly cancelled because each percentage is calculated on a different base value. Whenever a quantity is increased and then decreased by the same percentage, there is always a net decrease. The formula for successive percentage change is: \[ \text{Net Percentage Change} = a + b + \frac{ab}{100} \] where \(a\) and \(b\) are percentage changes with signs.

Step 1: Assume an initial value.
Let the original number be: \[ 100 \]

Step 2: Increase the number by 20%.
Increase: \[ 20% \text{ of } 100 = 20 \] New value becomes: \[ 100 + 20 = 120 \]

Step 3: Decrease the new value by 20%.
Now decrease 120 by 20%: \[ 20% \text{ of } 120 = 24 \] Therefore: \[ 120 - 24 = 96 \]

Step 4: Compare final value with original value.
Original value: \[ 100 \] Final value: \[ 96 \] Decrease: \[ 100 - 96 = 4 \] Percentage decrease: \[ \frac{4}{100}\times100 = 4% \]

Step 5: Write the final conclusion.
Hence, the overall result is: \[ \boxed{4% \text{ decrease}} \]