Practice › Number and Algebra › Using Percentages

Using Percentages: Paper 1 Long Questions

Ten Paper 1 questions on profit and loss, discount, percentage change, simple and compound interest, depreciation and salaries tax. The set opens with the Section A(1) patterns the exam uses most, and ends with two sub-types that sit in the syllabus but seldom appear in recent papers. Detailed solutions can be requested by email.

10 questions · 43 marks · about 45 minutes · answers below each question

All questions are original, written for Math and AI Academy and modelled on past-paper style. They are not reproductions of HKEAA examination questions.

Question 1 · Modelled on 2012 P1 Q4 — starts from the first person instead of the middle one, then tests a claim about the third comparison

The weekly allowance of Amy is $25%$ higher than that of Ben, while the weekly allowance of Ben is $40%$ lower than that of Carl. It is given that the weekly allowance of Amy is $$360$ .

(a) Find the weekly allowance of Ben.

(b) Carl claims that the weekly allowance of Amy is $25%$ lower than his. Do you agree? Explain your answer.

(4 marks)

Show answer

(a) $$288$

(b) Agreed. Carl's allowance is $$480$ , and $$360$ is $25%$ lower than $$480$ .

Each percentage is measured against the person named after the word "than".

Question 2 · Modelled on 2019 P1 Q5 — the cost is given and the percentage profit is asked, the reverse of the original part (b)

A backpack is sold at a discount of $35%$ on its marked price. The selling price of the backpack is $$416$ .

(a) Find the marked price of the backpack.

(b) It is given that the cost of the backpack is $$320$ . Find the percentage profit.

(4 marks)

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(a) $$640$

(b) $30%$

A discount is taken off the marked price; a percentage profit is measured against the cost.

Question 3 · Modelled on 2015 P1 Q6 — the article is sold at a loss instead of a profit

The cost of a lamp is $$450$ . The lamp is now sold and the percentage loss is $12%$ .

(a) Find the selling price of the lamp.

(b) If the lamp is sold at a discount of $28%$ on its marked price, find the marked price of the lamp.

(4 marks)

Show answer

(a) $$396$

(b) $$550$

A marked price above the cost does not guarantee a profit once the discount is taken off.

Question 4 · Modelled on 2024 P1 Q6 — asks for the selling price, so the cost has to be found first and then carried through both percentages

The marked price of a kettle is $60%$ higher than its cost. The kettle is sold at a discount of $30%$ on its marked price and the profit is $$54$ . Find the selling price of the kettle.

(4 marks)

Show answer

$$504$

Write the selling price as a multiple of the cost: $1.6 \times 0.7 = 1.12$ , so the profit is $12%$ of the cost.

Question 5 · Modelled on 2021 P1 Q6 — asks for the cost; the selling price is written in two ways and equated

The marked price of a jacket is higher than its cost by $$210$ . The jacket is sold at a discount of $20%$ on its marked price. After selling the jacket, the percentage profit is $15%$ . Find the cost of the jacket.

(4 marks)

Show answer

$$480$

The selling price is both $80%$ of the marked price and $115%$ of the cost.

Question 6 · Modelled on 2026 P1 Q5 — items are added rather than taken out, and the comparison is "more than" instead of "less than"

The sum of the number of fiction books and the number of non-fiction books in a library is $1160$ . If $140$ fiction books are added to the library, then the number of fiction books is $60%$ more than the number of non-fiction books. Find the original number of fiction books in the library.

(4 marks)

Show answer

$660$

The number of non-fiction books never changes, so it is the unknown to choose.

Question 7 · Modelled on 2015 P2 Q9 — turned into a long question, with a second part that runs the overall change backwards

The number of visitors to a museum increased by $20%$ from 2023 to 2024, and then decreased by $15%$ from 2024 to 2025.

(a) Find the percentage change in the number of visitors from 2023 to 2025.

(b) If the number of visitors in 2025 is $30600$ , find the number of visitors in 2023.

(4 marks)

Show answer

(a) An increase of $2%$

(b) $30000$

The two changes multiply: $1.2 \times 0.85 = 1.02$ . They do not add to $5%$ .

Question 8 · Modelled on 2017 P2 Q10 and 2013 P2 Q11 — simple interest, yearly compounding and half-yearly compounding are set side by side on one deposit

Karen deposits $$40 000$ in a bank at an interest rate of $5%$ per annum for 2 years.

(a) If simple interest is paid, find the interest.

(b) If the interest is compounded yearly, find the interest.

(c) If the interest is compounded half-yearly, find the amount correct to the nearest dollar.

(5 marks)

Show answer

(a) $$4000$

(b) $$4100$

(c) $$44 153$

Half-yearly compounding uses $2.5%$ per period for 4 periods, not $5%$ for 2.

Question 9 · New sub-type: depreciation — no direct past-paper model; the syllabus pairs depreciation with compound interest, and part (b) is a claim to test

The value of a car depreciates by $20%$ each year. The value of the car is now $$256 000$ .

(a) Find the value of the car 2 years ago.

(b) The owner claims that 3 years from now, the value of the car will be less than half of its present value. Do you agree? Explain your answer.

(5 marks)

Show answer

(a) $$400 000$

(b) Disagreed. The value will be $$131 072$ , which is more than half of $$256 000$ ( $$128 000$ ).

Three falls of $20%$ leave $0. 8^{3} = 0.512$ of the value, not $1 - 0.6 = 0.4$ .

Question 10 · New sub-type: salaries tax — no direct past-paper model; progressive tax bands are in the junior syllabus, and part (b) reads the table backwards

In a city, salaries tax is charged on the net chargeable income of a person at the following rates:

on the first $$50 000$ : $2%$
on the next $$50 000$ : $6%$
on the next $$50 000$ : $10%$
on the remainder: $14%$

(a) The net chargeable income of Ms Ng is $$130 000$ . Find her salaries tax payable.

(b) The salaries tax payable by Mr Lee is $$11 800$ . Find his net chargeable income.

(5 marks)

Show answer

(a) $$7000$

(b) $$170 000$

Each rate applies only to the slice of income inside its own band.

Continue practising this topic: Try the Paper 1 Challenge for harder variants, or move to Paper 2 multiple-choice — also available as Paper 2 Challenge MC.

Where this sits in the syllabus

Using Percentages is junior secondary content that the HKDSE keeps examining. In most years from 2012 to 2026, Paper 1 Section A(1) carries a short profit-and-discount or percentage-change question, and Paper 2 often carries a compound interest item. These marks are among the most reachable on the paper, and they are usually lost on one thing: taking a percentage of the wrong amount.

Full coverage of this topic, and the rest of the course, is on the Mathematics page. More sets are listed on the practice index.

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