Percentages are used to describe increases, decreases, profit, loss, and tax. GCSE Maths requires you to calculate percentage change and work backwards to find original amounts (reverse percentages).
Core Concepts
Percentage Change
Multiplier Method
- Increase by 15%: multiply by
- Decrease by 20%: multiply by
- General: increase by → multiply by
Reverse Percentages
Finding the original value when you know the result after a percentage change.
Example: After a 20% increase, the price is £60. Find the original price.
→
Repeated Percentage Change
For compound changes, multiply the multipliers:
3% increase per year for 5 years:
Worked Example: Example 1
A shirt costs £40. It increases by 25%. New price: .
Worked Example: Example 2
After a 15% discount, a laptop costs £510. Original: .
Worked Example: Example 3
A car loses 12% of its value each year. Worth £20,000 now. Value in 3 years: .
Practice Problems
- Increase £250 by 30%.
- After a 10% increase, a bill is £55. Find the original.
- A population of 5000 decreases by 5% per year. Population after 4 years?
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Key Takeaways
Percentage change = change ÷ original × 100.
Use multipliers for efficient calculation.
Reverse percentages: divide by the multiplier to find the original.
Compound changes: raise the multiplier to the power of the number of periods.