Percentage Increase – Formula and Applications
A percentage increase happens when a value goes up. You calculate how much it has risen, then express that rise as a percentage of the original value. This skill is used whenever you compare growth — in prices, populations, salaries, and more.
The Formula
Percentage Increase = (Increase / Original Value) times 100
where Increase = New Value minus Original Value.
Step-by-Step Method
Increase = 65 - 50 = 15. Percentage increase = (15 / 50) times 100 = 30%.
Increase = 8600 - 8000 = 600. Percentage increase = (600 / 8000) times 100 = 7.5%.
Increase = 27600 - 24000 = 3600. (3600 / 24000) times 100 = 15%.
Applying a Percentage Increase
Sometimes you are given the original value and asked to find the new value after a percentage increase.
New Value = Original times (1 + Percentage/100)
The multiplier for a 25% increase is 1.25.
New value = 80 times 1.20 = £96.
New population = 12,000 times 1.08 = 12,960 people.
Common Multipliers Table
| % Increase | Multiplier |
|---|---|
| 5% | 1.05 |
| 10% | 1.10 |
| 15% | 1.15 |
| 20% | 1.20 |
| 25% | 1.25 |
| 50% | 1.50 |
| 100% | 2.00 |
Real-Life Uses
- Inflation: prices rising 4% per year.
- Pay rise: salary increasing 6%.
- Population growth: a city expanding 2.5% annually.
- Investment returns: a fund growing 12% in a year.
Key Takeaways
- Percentage increase = (increase / original) times 100.
- Always divide by the original value, not the new one.
- To find the new value: multiply original by (1 + rate/100).
- A 100% increase means the value doubles.
Practice Questions
- A book costs £12 and the price rises to £15. What is the percentage increase?
- A factory produced 4200 units last year and 4620 this year. What is the percentage increase?
- Increase 240 by 35%.
- A house valued at £250,000 increases in value by 6%. What is it now worth?
- A cyclist rides 40 km on Monday and 52 km on Tuesday. Find the percentage increase.