Question

A number is increased by 25% and then decreased by 20%. What is the net % change?

• A. 0%
• B. 2%
• C. 5%
• D. 10%

Hint:

When successive percentage increases and decreases are applied, multiply the corresponding multipliers: \[ (1 + \frac{p}{100}) \times (1 - \frac{q}{100}) \] to find the net effect.

Answer 1

The Correct Option is A

Step 1: Calculate the effect of 25% increase.
If the original number is \( x \), after a 25% increase, it becomes: \[ x \times \left(1 + \frac{25}{100}\right) = 1.25x. \] Step 2: Calculate the effect of 20% decrease on the new number. After decreasing by 20%, the number becomes: \[ 1.25x \times \left(1 - \frac{20}{100}\right) = 1.25x \times 0.8 = 1.0x. \] Step 3: Find the net change.
The final number is \( 1.0x \), which is the same as the original number \( x \). So, the net percentage change is: \[ \frac{1.0x - x}{x} \times 100% = 0%. \]