Question

A number is increased by 25 and then decreased by 25. What is the net percentage change?

• A. 6.25 decrease
• B. 6.25 increase
• C. No change
• D. 3.125 decrease

Hint:

For successive percentage changes, use $1 - \left(\frac{a}{100}\right)^2$ for equal increase/decrease.

Answer 1

The Correct Option is A

- Step 1: Assume number. Let number = 100.
- Step 2: Increase by 25. $100 \cdot 1.25 = 125$.
- Step 3: Decrease by 25. $125 \cdot 0.75 = 93.75$.
- Step 4: Net change. Change = $93.75 - 100 = -6.25$. Percentage = $\frac{-6.25}{100} \times 100 = -6.25$.
- Step 5: Formula. Net effect: $\left(1 + \frac{25}{100}\right) \cdot \left(1 - \frac{25}{100}\right) = 1.25 \cdot 0.75 = 0.9375$. Decrease = $1 - 0.9375 = 0.0625 = 6.25$.
- Step 6: Conclusion. Option (1) 6.25 decrease is correct.