% of, % change, reverse %, successive %, percentage points, shares of a total.
Percentage change = (new − old) ÷ old × 100. Always divide by the original (earlier) value.
By what percentage did Greenfield Retail's revenue change from 2023 to 2024?
Answer: 25.0%
Percentage change = (new − old) ÷ old × 100. Here (400 − 320) ÷ 320 = 80 ÷ 320 = 0.25 = 25.0%. The 20.0% foil divides the rise by the new value (400) instead of the original. The 22.2% foil divides by the average of the two years (360). The 11.1% foil divides by the two years summed (720). The 125.0% foil reports 2024 as a percentage of 2023 (400/320) rather than the change.
Apply the shares in turn: multiply the total by the first percentage, then multiply that result by the second.
A pension fund is worth £219m. Commodities make up 4.8% of the fund; within Commodities, High Grade Copper is 13.1%. What is the value of the High Grade Copper holding?
Answer: £1.38m
Apply the shares in turn: Commodities = 219 × 4.8% = £10.51m; High Grade Copper = 10.51 × 13.1% = £1.38m. The £10.51m foil stops at the first level; £28.69m applies 13.1% to the whole fund; £39.20m adds the two percentages.
Share = part ÷ total × 100, using the overall total as the denominator.
Digital makes up what percentage of the total £500,000 marketing budget?
Answer: 36.0%
Digital is 180 of the 500 total: 180/500 = 36.0%. The 30.0% and 16.0% foils read the wrong channel; 56.3% divides by the other channels (320) instead of the total; 18.0% doubles the total.
x% of y = (x ÷ 100) × y.
What is 35% of 1,240?
Answer: 434
35% of 1,240 = 0.35 × 1,240 = 434. The 806 foil takes the other 65%; 124 uses 10%; 4,340 multiplies by 3.5 (decimal slip); 354 divides instead.
The given value already includes the change, so divide by (1 + rate) — don't subtract the percentage from it.
After a 15% increase, a product now costs £92. What was the original price?
Answer: 80.00
The £92 is 115% of the original, so original = 92 ÷ 1.15 = £80.00. The £78.20 foil takes 15% off the new price (forward, not reverse); £105.80 increases it again; the others divide by the wrong factor.
Successive percentages multiply: apply each factor in turn (e.g. ×1.10 then ×1.20). They never simply add.
A coat is reduced by 20% in a sale. At the till, a loyalty card takes a further 10% off the reduced price. The customer pays £108. What was the original price?
Answer: £150.00
The £108 is 80% × 90% = 72% of the original, so original = 108 ÷ 0.72 = £150.00. Traps: £154.29 treats the discounts as a single additive 30% (÷0.70); £135 and £120 reverse only one of the two discounts; £77.76 applies the discounts forward instead of reversing them.
A VAT-inclusive price is (100% + rate) of the net price, so net = gross ÷ (1 + rate).
A price including 20% VAT is £96. What is the price excluding VAT?
Answer: £80.00
The £96 is 120% of the net price, so net = 96 ÷ 1.20 = £80.00. The £76.80 foil takes 20% off the gross; £115.20 adds VAT again; £19.20 and £16.00 give a VAT amount, not the net price.
Percentage points = the simple difference between two percentages (subtract them). The relative percentage change is a different number.
Sale price = original price × (1 − discount rate).
Selling price = cost × (1 + markup rate).
Overall change uses the endpoints only: (final − first) ÷ first. Yearly percentages compound — they don't add.
A company's revenue was £200m in 2021, £220m in 2022, £242m in 2023 and £266.2m in 2024. By what percentage did revenue change overall from 2021 to 2024?
Answer: 33.1%
Overall change uses the endpoints: (266.2 − 200)/200 = 33.1%. The 30% foil adds the three yearly 10% changes (they compound, not add); 10% is one year only.
Apply each step as a multiplier in sequence (× (1 + markup), then × (1 − discount)); they don't net off additively.
A jacket is marked up 40% from its £50 cost, then discounted 25% in a sale. What is the sale price?
Answer: £52.50
Mark up: 50 × 1.40 = £70. Discount: 70 × 0.75 = £52.50. The £57.50 foil treats it as a net 15%; £70 stops after the markup; £37.50 discounts the cost; £45 subtracts £25 instead of 25%.
Combine the changes into one net factor (multiply them), then divide the final value by that factor.
A price is marked up 20%, then discounted 15% on the new price, giving a final price of £102. What was the original price?
Answer: £100
The £102 is 1.20 × 0.85 = 1.02 of the original, so original = 102 ÷ 1.02 = £100. The £105 foil treats it as a net 5% (additive); £104.04 applies the changes forward instead of reversing.
Compute the share in each period (part ÷ that period's total), then the percentage change between the shares.
Product X's sales were £120m of a £480m total in 2022, and £180m of a £600m total in 2024. By what percentage did Product X's SHARE of total sales change?
Answer: 20.0%
Shares: 120/480 = 25% and 180/600 = 30% (the total changed too). Change in share = (30−25)/25 = 20%. The 5.0% foil gives percentage points; 50% uses the raw sales (ignoring that the total grew).