Net Percentage Change for Equal Increase/Decrease
- Trick / Shortcut
- Net Percentage Change for Equal Increase/Decrease
- Topic
- Percentages
- How It Works
If a value is first increased by $x%$ and then decreased by $x%$, the net change is always a decrease.
Net Change Formula: $- \left(\frac{x^2}{100}\right)%$
This formula quantifies the net loss. It shows that successive equal percentage changes do not cancel each other out to zero net change.
- Example
A price increases by $20%$ and then decreases by $20%$.
Using the formula, $x = 20$: Net Change $= - \left(\frac{20^2}{100}\right)% = - \left(\frac{400}{100}\right)% = \textbf{-4%}$
This means there is a net $\mathbf{4%}$ decrease.
Example calculation: Starting with NPR 100:
- Increase by $20%$ ($100 \times 1.20 = 120$)
- Decrease by $20%$ ($120 \times 0.80 = 96$)
The final value is NPR 96, which is a $4%$ decrease from the original NPR 100.