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Ratio & Proportion · Foundation & Higher

Percentage increase & decrease

Percentage increase and decrease are used to find a new amount after a percentage change. The multiplier method is the most efficient approach.

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Key facts to remember

  • 1Multiplier for x% increase = 1 + x/100 (e.g. 15% increase → × 1.15).
  • 2Multiplier for x% decrease = 1 − x/100 (e.g. 20% decrease → × 0.80).
  • 3Percentage change = (change ÷ original) × 100.
  • 4Multiple percentage changes: apply each multiplier in sequence.
  • 5Two successive 10% increases ≠ a 20% increase (you need 1.1 × 1.1 = 1.21, i.e. 21%).
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Formulas

Percentage change
% change = (new − original) / original × 100
New value
New value = original × multiplier
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Worked examples

Example 1

A TV costs £480. It is reduced by 15%. Find the sale price.

Working

  1. Multiplier = 1 − 0.15 = 0.85
  2. Sale price = 480 × 0.85 = £408
Answer£408
Example 2

A house bought for £200,000 is now worth £230,000. Find the percentage change.

Working

  1. Change = 230,000 − 200,000 = 30,000
  2. % change = (30,000 ÷ 200,000) × 100 = 15%
Answer15% increase
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Common mistakes

✗Adding the percentage of the new value rather than the original value.
✗Using the wrong multiplier — a 20% decrease uses 0.80, not 0.20.
✗Forgetting to state whether a percentage change is an increase or decrease.
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Exam tips

✓Use the multiplier method — it's quicker and less error-prone than finding the percentage and adding/subtracting.
✓For percentage change: always divide by the original, not the new value.

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