Percentage word problems (exam style)
Weight change, profit and successive discounts with numbers in the spirit of S3 assessment items.
Key formulas
Read the base carefully
“Increased by 10%” uses last year’s value as base. “Increased to 110%” already states the new relative size. Underline the base sentence before calculating.
Profit, loss and discount
Profit/loss percentages almost always use cost price. Discount uses marked price. Mixing the bases is the most common exam error.
Two-step stories
A marked-up item then discounted needs two multipliers. Compute the overall multiplier, then interpret as a single percentage change if asked.
Exam habit
Write a one-line “model” with multipliers before substituting Hong Kong dollar amounts.
Worked example
Percentage increase
Problem. Ken weighed 64 kg last year and 72 kg this year. Find the percentage increase.
Solution. Change = 8. Percentage = 8/64 × 100% = 12.5%.
Review quiz
1 / 464 kg → 72 kg. Percentage increase?
Practice questions
- Last year Ken weighed 64 kg. This year he weighs 72 kg. Find the percentage increase.
- Cost $950, sold at 12% loss. Find the selling price.
- Marked $1680, successive discounts 10% then 5%. Find the selling price.
- A shopkeeper buys for $500 and wants 20% profit after allowing a 10% discount on the marked price. Find the marked price.
Study notes
Do successive 10% and 5% equal 15%?
No — multipliers 0.9 × 0.95 = 0.855, i.e. 14.5% off overall.
Percentage change formula uses which value?
Always the original value in the denominator.