Question:
If a number is increased by 30% and then decreased by 20%, what is the net change?
If a number is increased by 30% and then decreased by 20%, what is the net change?
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When successive percentage changes are applied, calculate the effect step by step using the new value each time, not just by adding the percentages.
Updated On: Oct 18, 2025
- 4% increase
- 6% increase
- 8% increase
- 6% decrease
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The Correct Option is A
Solution and Explanation
Let the original number be \( x \).
- After a 30% increase, the number becomes \( x + 0.30x = 1.30x \).
- Then, a 20% decrease is applied to \( 1.30x \), which results in \( 1.30x - 0.20(1.30x) = 1.30x \times 0.80 = 1.04x \).
Thus, the final number is \( 1.04x \), which represents a 4% increase from the original number.
Therefore, the net change is a 4% increase.
- After a 30% increase, the number becomes \( x + 0.30x = 1.30x \).
- Then, a 20% decrease is applied to \( 1.30x \), which results in \( 1.30x - 0.20(1.30x) = 1.30x \times 0.80 = 1.04x \).
Thus, the final number is \( 1.04x \), which represents a 4% increase from the original number.
Therefore, the net change is a 4% increase.
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