Question

The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

• A. 40
• B. 35
• C. 45
• D. 50

Hint:

When dealing with percentage increase and decrease, convert them into decimal multipliers. Then subtract or equate as needed.

Answer 1

The Correct Option is A

Step 1: Let the original number be \( x \). Step 2: Calculate increased and decreased values. \[ \text{25% increase of } x = x + \frac{25}{100}x = \frac{125}{100}x = 1.25x \] \[ \text{30% decrease of } x = x - \frac{30}{100}x = \frac{70}{100}x = 0.7x \] Step 3: Use the given condition. \[ \text{Difference} = 1.25x - 0.7x = 0.55x = 22 \Rightarrow x = \frac{22}{0.55} = 40 \]