Question

A company's revenue increased by 20% in the first year and then decreased by 10% in the second year. What is the net percentage change in revenue over the two years?

• A. 8% increase
• B. 10% increase
• C. 12% increase
• D. 15% increase
• E. 30% increase

Hint:

The formula \( (x + y + xy/100)% \) is extremely useful and fast for any problem involving two successive percentage changes. Remember to use negative signs for decreases.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem deals with successive percentage changes. A common mistake is to simply add the percentages (20% - 10% = 10%). However, the second percentage change is calculated on the new value after the first change, not the original value.
Step 2: Key Formula or Approach:
Let the initial revenue be \(R\). We can track the changes over the two years. A good strategy is to assume an initial value of 100.
For successive percentage changes of \(x%\) and \(y%\), the net change is given by the formula: \( \left( x + y + \frac{xy}{100} \right)% \).
Step 3: Detailed Explanation:
Method 1: Assuming an Initial Value
Let the initial revenue be \$100.
In the first year, revenue increases by 20%:
\[ \text{Revenue after Year 1} = 100 + (20% \text{ of } 100) = 100 + 20 = \$120 \]
In the second year, this new revenue decreases by 10%:
\[ \text{Decrease in Year 2} = 10% \text{ of } 120 = 0.10 \times 120 = \$12 \]
\[ \text{Revenue after Year 2} = 120 - 12 = \$108 \]
The net change is from the original \$100 to the final \$108.
\[ \text{Net Change} = 108 - 100 = \$8 \]
\[ \text{Net Percentage Change} = \frac{\text{Net Change}}{\text{Original Value}} \times 100% = \frac{8}{100} \times 100% = 8% \]
Since the final value is higher, it is an 8% increase.
Method 2: Using the Formula
Let \(x = +20\) (increase) and \(y = -10\) (decrease).
\[ \text{Net Change} = \left( 20 + (-10) + \frac{(20)(-10)}{100} \right)% = \left( 10 - \frac{200}{100} \right)% = (10 - 2)% = 8% \]
A positive result indicates a net increase.
Step 4: Final Answer:
The net percentage change is an 8% increase, which corresponds to option (A).