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. 70
• B. 65
• C. 40
• D. 90

Answer 1

The Correct Option is C

Let the original number be denoted as \( x \). 

1. Calculate the value of the number increased by 25%:

\( x + 0.25x = 1.25x \)

2. Calculate the value of the original number decreased by 30%:

\( x - 0.30x = 0.70x \)

3. The difference between these two values is given as 22:

\( 1.25x - 0.70x = 22 \)

4. Simplify the equation:

\( 0.55x = 22 \)

5. Solve for \( x \):

\( x = \frac{22}{0.55} \)

\( x = 40 \)

Thus, the original number is 40.