Answer :
Answer:
Step-by-step explanation:
To find the net increase or decrease percentage when a number is increased by 30%, we can use the formula for percentage change:
\[ \text{Percentage Change} = \left( \frac{\text{Change in Value}}{\text{Original Value}} \right) \times 100\% \]
In this case, the original value is the number itself, and the change in value is the increase of 30%.
When a number is increased by 30%, the new value becomes the original value plus 30% of the original value.
So, if the original number is \( x \), the new value is \( x + 0.30x = 1.30x \).
Now, let's calculate the percentage change:
\[ \text{Percentage Change} = \left( \frac{1.30x - x}{x} \right) \times 100\% \]
\[ \text{Percentage Change} = \left( \frac{0.30x}{x} \right) \times 100\% \]
\[ \text{Percentage Change} = 30\% \]
Therefore, when a number is increased by 30%, the net increase percentage is 30%.
Increasing a number by 30% followed by a decrease of 30% results in a net decrease. The overall change is not a simple
subtraction of the two percentages. Let's consider an example:
* If the original number is 100, a 30% increase makes it 130.
* Decreasing 130 by 30% gives you 91.
There's a net decrease of 9 from the original number (100). This translates to a 9% decrease.
We can use a formula to calculate the net change for any increase (a%) followed by a decrease (b%):
Net change = (a - b - ab/100)%
In this case, a = 30 and b = 30, so the net change is -9%.
subtraction of the two percentages. Let's consider an example:
* If the original number is 100, a 30% increase makes it 130.
* Decreasing 130 by 30% gives you 91.
There's a net decrease of 9 from the original number (100). This translates to a 9% decrease.
We can use a formula to calculate the net change for any increase (a%) followed by a decrease (b%):
Net change = (a - b - ab/100)%
In this case, a = 30 and b = 30, so the net change is -9%.