Percentage increase and decrease is a core topic in GCSE Maths, appearing on all major exam boards like AQA, Edexcel, and OCR. Whether it's calculating a price rise, a discount in a sale, or a change in population, mastering this skill is essential. This guide breaks it down into simple, manageable steps.
The Core Concept: What is a Percentage Change?
A percentage change tells us how much a quantity has grown or shrunk relative to its original value. It's always expressed as a percentage of the original amount. This is a key idea: the "original" or "old" value is our 100% baseline.
The Essential Formula
For any percentage change problem, you can use this single, powerful formula:
** Percentage Change = Change/Original × 100
Where:
Change = New Value – Original Value (this can be positive for an increase, negative for a decrease).
- Original = The starting value (100%).
flowchart TD
A["Start: Identify Original and New Values"] --> B["Is New > Original?"]
B -- Yes --> C["Change = New - Original, It is an INCREASE"]
B -- No --> D["Change = Original - New, It is a DECREASE"]
C --> E["Apply Formula:, Percentage Change = Change / Original x 100"]
D --> E
E --> F["State answer with %, and 'increase' or 'decrease'"]
Step-by-Step Walkthrough
Example 1: Calculating a Percentage Increase
A town's population grew from 12,500 to 13,200. What is the percentage increase?
Identify the Original and New values.
Original (Old) = 12,500
- New = 13,200
Calculate the Change.
- Change = New – Original = 13,200 – 12,500 = 700
Apply the Formula.
Percentage Change = (Change / Original) × 100
- = (70012,500) × 100
Calculate.
700 ÷ 12,500 = 0.056
- 0.056 × 100 = 5.6
State the final answer clearly.
- The population increased by 5.6%.
Example 2: Calculating a Percentage Decrease
In a sale, a coat was reduced from £84 to £63. What is the percentage discount?
Identify the Original and New values.
Original = £84
- New = £63
Calculate the Change (the discount amount).
- Change = Original – New = 84 – 63 = 21
(We use Original – New here because it's a decrease.)
Apply the Formula.
- Percentage Change = (2184) × 100
Calculate.
21 ÷ 84 = 0.25
- 0.25 × 100 = 25
State the final answer clearly.
- The coat has a 25% discount.
The Multiplier Method: A Faster Way
For finding a new value after a change, the multiplier method is incredibly efficient and is heavily favoured in GCSE exams.
For an increase of 15%: You find 115% of the original. The multiplier is 1.15 (because 100% + 15% = 115% = 1.15).
- For a decrease of 15%: You find 85% of the original. The multiplier is 0.85 (because 100% – 15% = 85% = 0.85).
Example 3: Using the Multiplier for an Increase
Increase £240 by 17%.
Find the multiplier. 100% + 17% = 117% = 1.17
Multiply. New Value = Original × Multiplier = £240 × 1.17
- Calculate. £240 × 1.17 = £280.80
Example 4: Using the Multiplier for a Decrease
Decrease 360kg by 12%.
Find the multiplier. 100% – 12% = 88% = 0.88
Multiply. New Value = 360 × 0.88
- Calculate. 360 × 0.88 = 316.8 kg
Reverse Percentages: Working Backwards
This is a common exam challenge: "After a 20% increase, a house is worth £240,000. What was its original price?"
The golden rule: Find the multiplier that was used, then ÷ by it to go backwards.
Example 5: Reverse Percentage Problem
After a 15% discount, a laptop costs £425. What was its original price?
Analyse the change. A 15% discount means you paid 85% of the original price.
- Multiplier = 0.85
Set up the equation.
- Original Price × 0.85 = £425
Solve by dividing.
- Original Price = £425 ÷ 0.85
Calculate.
- £425 ÷ 0.85 = £500
- Check: 15% of £500 is £75. £500 – £75 = £425. ✓
Common Pitfalls and How to Avoid Them
Confusing Increase and Decrease Multipliers: Always remember: Increase = >1, Decrease = <1. Write "100% ± %" first to be sure.
Using the Wrong 'Original' Value: In percentage change, the denominator is always the old/original value, not the new one.
Forgetting the '× 100': The formula gives you a decimal. Multiplying by 100 converts it to a percentage.
- Reverse Percentage Errors: Remember, if you multiplied to go forward, you must ÷ to go back. Do not multiply by the inverse multiplier (e.g., don't multiply by 1.15 to reverse a 15% increase).
Practice for Your Exam
Try these typical GCSE questions:
A car's value depreciates by 8% each year. If it was bought for £9,500, what is its value after one year?
A salary of £28,000 is increased by 3.5%. What is the new salary?
A shop advertises "£20 off" a table. If the sale price is £120, what is the percentage discount?
- Challenge (Reverse %): A restaurant adds a 10% service charge to a bill. The total paid is £49.50. What was the bill before the service charge?
Answers:
£9,500 × 0.92 = £8,740
£28,000 × 1.035 = £28,980
Original price = £120 + £20 = £140. Discount % = (20140) × 100 = 14.3% (to 1 d.p.)
- Multiplier = 1.10. Original bill = £49.50 ÷ 1.10 = £45
- By learning the formula, mastering the multiplier method, and practising reverse percentages, you'll be well-prepared to tackle any percentage change question in your GCSE Maths exam. Good luck with your revision!