GCSE Maths Percentage Change & Reverse Percentages

GCSE Maths: Percentage change

Percentage change appears everywhere in GCSE Maths — from shop discounts to interest and data questions. Examiners reward clear structure: find the change, divide by the original, then multiply by 100. Reverse percentages are the same idea backwards: treat the new amount as a percentage of the original you do not yet know.

Worked examples

Example 1
Basic increase
A £40 jacket increases in price by 15%. Change = 0.15 × £40 = £6. New price = £40 + £6 = £46. As one multiplier: £40 × 1.15 = £46.
Example 2
Reverse percentage (after a sale)
After a 20% reduction, a console costs £360. What was the original price? Sale price is 80% of original → 0.8 × original = £360. Original = £360 ÷ 0.8 = £450. Check: 20% off £450 is £90, leaving £360.

Mini quiz (3 questions)

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1. A stock rises from £50 to £58. What is the percentage increase?
- A.8%
- B.16%
- C.14%
- D.12%
Show answer
Correct: 16%
Change = £8. 8/50 = 0.16 → 16%.
2. A population falls by 30% to 14,000. What was the population before the fall?
- A.18,200
- B.20,000
- C.22,000
- D.19,600
Show answer
Correct: 20,000
New = 70% of old → old = 14,000 ÷ 0.7 = 20,000.
3. Which step is always wrong for percentage change?
- A.Dividing the change by the new value
- B.Dividing the change by the original value
- C.Multiplying the decimal by 100
- D.Labelling increase vs decrease
Show answer
Correct: Dividing the change by the new value
Percentage change uses the original value as the denominator.

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Percentage change & reverse percentages