Question:
If the price of an item is increased by 20% and then decreased by 20%, what is the net percentage change in the price?
If the price of an item is increased by 20% and then decreased by 20%, what is the net percentage change in the price?
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For successive percentage changes of \( +x% \) and \( -x% \), there is a shortcut formula for the net change: \( \text{Net Change %} = \left( \frac{x}{10} \right)^2 \) decrease.
In this case, \( x = 20 \), so the net change is a \( \left( \frac{20}{10} \right)^2 = 2^2 = 4% \) decrease.
Updated On: Oct 4, 2025
- 4% decrease
- 4% increase
- 0%
- 20% decrease
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
This problem deals with successive percentage changes. It's important to remember that the second percentage change is calculated on the new price, not the original price.
Step 2: Key Formula or Approach:
Let's assume an initial price for the item to make the calculation concrete. A good choice is $100.
Step 3: Detailed Explanation:
Step 3a: Calculate the price after the increase.
Let the original price be $100.
The price is increased by 20%.
Increase amount = \( 20% \text{ of } 100 = \frac{20}{100} \times 100 = $20 \).
New price = Original price + Increase = $100 + $20 = $120.
Step 3b: Calculate the price after the decrease.
The new price of $120 is now decreased by 20%.
Decrease amount = \( 20% \text{ of } 120 = \frac{20}{100} \times 120 = 0.2 \times 120 = $24 \).
Final price = New price - Decrease = $120 - $24 = $96.
Step 3c: Calculate the net percentage change.
The price changed from an original of $100 to a final of $96.
The change in price is $96 - $100 = -$4.
The percentage change = \( \frac{\text{Change}}{\text{Original Price}} \times 100 = \frac{-4}{100} \times 100 = -4% \).
A negative sign indicates a decrease.
Step 4: Final Answer:
The net change is a 4% decrease.
This problem deals with successive percentage changes. It's important to remember that the second percentage change is calculated on the new price, not the original price.
Step 2: Key Formula or Approach:
Let's assume an initial price for the item to make the calculation concrete. A good choice is $100.
Step 3: Detailed Explanation:
Step 3a: Calculate the price after the increase.
Let the original price be $100.
The price is increased by 20%.
Increase amount = \( 20% \text{ of } 100 = \frac{20}{100} \times 100 = $20 \).
New price = Original price + Increase = $100 + $20 = $120.
Step 3b: Calculate the price after the decrease.
The new price of $120 is now decreased by 20%.
Decrease amount = \( 20% \text{ of } 120 = \frac{20}{100} \times 120 = 0.2 \times 120 = $24 \).
Final price = New price - Decrease = $120 - $24 = $96.
Step 3c: Calculate the net percentage change.
The price changed from an original of $100 to a final of $96.
The change in price is $96 - $100 = -$4.
The percentage change = \( \frac{\text{Change}}{\text{Original Price}} \times 100 = \frac{-4}{100} \times 100 = -4% \).
A negative sign indicates a decrease.
Step 4: Final Answer:
The net change is a 4% decrease.
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