Percentage Decrease – Formula and Applications
A percentage decrease happens when a value falls. You express how much it has fallen as a percentage of the original value. This appears in sales, depreciation, weight loss, and many other everyday situations.
The Formula
Percentage Decrease = (Decrease / Original Value) times 100 where Decrease = Original Value minus New Value.
Worked Examples
A price falls from 120 to 90. Find the percentage decrease.
Decrease = 120 - 90 = 30. (30 / 120) times 100 = 25%.
A car depreciates from 18,000 to 13,500.
Decrease = 18000 - 13500 = 4500. (4500 / 18000) times 100 = 25%.
Rainfall drops from 85 mm to 51 mm.
Decrease = 85 - 51 = 34. (34 / 85) times 100 = 40%.
Applying a Percentage Decrease
New Value = Original times (1 - Percentage/100). The multiplier for a 30% decrease is 0.70.
Decrease 200 by 15%
New value = 200 times 0.85 = 170.
A TV worth 640 loses 35% of its value.
640 times 0.65 = 416.
Common Multipliers Table
| % Decrease | Multiplier |
|---|---|
| 5% | 0.95 |
| 10% | 0.90 |
| 20% | 0.80 |
| 25% | 0.75 |
| 30% | 0.70 |
| 50% | 0.50 |
Key Takeaways
- Percentage decrease = (decrease / original) times 100.
- Always divide by the original value, not the new one.
- To find the new value after a decrease: multiply original by (1 - rate/100).
- A 100% decrease means the value falls to zero.
Practice Questions
- A jacket falls from 75 to 60. What is the percentage decrease?
- A town population drops from 20,000 to 17,000. Find the percentage decrease.
- Decrease 560 by 12.5%.
- A laptop cost 800 last year and now costs 560. Find the percentage decrease.
- A cyclist training time drops from 5 hours to 3.5 hours a week. What is the percentage decrease?