Percentage change and reverse percentages

Percentages appear on every OCR J560 paper. Reverse percentages (finding the original amount) and percentage change (expressing a change as a percentage) are the two most commonly tested higher-tier topics.

Percentage change

Percentage change = (change ÷ original) × 100

Example: Price rises from £40 to £47. Percentage increase = (7 ÷ 40) × 100 = 17.5%.

Example: Population falls from 2,500 to 2,200. Percentage decrease = (300 ÷ 2500) × 100 = 12%.

Percentage of an amount

Direct calculation: 35% of £820 = 0.35 × 820 = £287.

Or: 10% = 82; 35% = 3.5 × 82 = 287. ✓

Percentage increase/decrease

Multiplier method (most efficient):

• Increase by 15%: × 1.15.
• Decrease by 25%: × 0.75.
• Increase by 7.5%: × 1.075.

Example: Increase £360 by 12% → 360 × 1.12 = £403.20.

Reverse percentages (finding the original)

If a value AFTER a percentage change is given, divide by the multiplier.

Example: After a 20% increase, the price is £84. What was the original price? Original × 1.20 = 84 → Original = 84 ÷ 1.20 = £70.

Example: After a 15% reduction in a sale, a coat costs £102. Find the original price. Original × 0.85 = 102 → Original = 102 ÷ 0.85 = £120.

Common error: subtracting 15% from £102 to get the original. WRONG. The 15% is taken off the ORIGINAL price, not the sale price.

VAT problems

VAT is added to the pre-VAT price. To find the pre-VAT price from a VAT-inclusive price (VAT at 20%): Pre-VAT = VAT-inclusive ÷ 1.20.

Comparing percentage changes

Percentage change always uses the original as the denominator. Use the same original for fair comparison.

Common OCR exam mistakes

1. Calculating percentage change using the wrong denominator (new value instead of original).
2. Reverse percentage: trying to subtract/add the percentage from the given value — must use the multiplier method.
3. Successive percentages: not compounding correctly. Two successive 10% increases ≠ 20% increase. See R16 (compound interest).