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Using Percentages: Paper 2 Multiple-Choice

Ten Paper 2 multiple-choice questions on percentage change, compound and simple interest, profit and discount, weighted percentages and depreciation. Every wrong option is the result of a common slip, so check which one you would have picked. Detailed solutions can be requested by email.

10 questions · about 15 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 2015 P2 Q9 — an increase followed by a decrease whose product is a small gain

If the price of a ticket is increased by $40%$ and then decreased by $25%$ , find the percentage change in the price of the ticket.

$5%$
$10%$
$15%$
$65%$

Show answer

A. $1.4 \times 0.75 = 1.05$ , an overall increase of $5%$ . Subtracting $40 - 25$ gives $15%$ , which ignores that the $25%$ is taken from the higher price.

Question 2 · Modelled on 2015 P2 Q10 — new sum, rate and period; the distractors are the simple, yearly and monthly amounts

A sum of $$30 000$ is deposited at an interest rate of $8%$ per annum for 2 years, compounded quarterly. Find the amount correct to the nearest dollar.

$$34 800$
$$34 992$
$$35 150$
$$35 187$

Show answer

C. Quarterly means $2%$ per period for 8 periods: $$30 000 (1.02)^{8} \approx $35 150$ .

Question 3 · New sub-type: simple interest — no direct past-paper model; the amount is given and the principal is asked

A sum of money is deposited at a simple interest rate of $4%$ per annum. After 5 years, the amount is $$27 000$ . Find the sum of money deposited.

$$21 600$
$$22 192$
$$22 500$
$$25 920$

Show answer

C. The amount is $1 + 5 \times 4% = 1.2$ times the principal, so the principal is $$27 000 \div 1.2$ .

Question 4 · Modelled on 2026 P2 Q11 — half-yearly instead of quarterly, with the yearly and simple-interest principals as distractors

A sum of $$ P$ is deposited at an interest rate of $6%$ per annum for 3 years, compounded half-yearly. If the amount is $$50 000$ , find $P$ correct to the nearest integer.

$41000$
$41874$
$41981$
$42373$

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B. $P (1.03)^{6} = 50000$ , so $P = 50000 \div (1.03)^{6} \approx 41874$ .

Question 5 · Modelled on 2016 P2 Q10 — the last amount in the chain is given, so the chain is followed forwards rather than undone

The monthly rent of flat $A$ is $30%$ higher than that of flat $B$ while the monthly rent of flat $B$ is $30%$ lower than that of flat $C$ . It is given that the monthly rent of flat $C$ is $$20 000$ . The monthly rent of flat $A$ is

$$18 200$ .
$$20 000$ .
$$21 800$ .
$$26 000$ .

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A. $B = $20 000 \times 0.7 = $14 000$ and $A = $14 000 \times 1.3 = $18 200$ . The two $30%$ figures do not cancel.

Question 6 · New sub-type: reversing a comparison — no direct official past-paper model; a "heavier than" statement is turned into the matching "lighter than" statement

The weight of parcel $P$ is $60%$ heavier than that of parcel $Q$ . Then the weight of parcel $Q$ is

$60%$ lighter than that of parcel $P$ .
$62.5%$ lighter than that of parcel $P$ .
$40%$ lighter than that of parcel $P$ .
$37.5%$ lighter than that of parcel $P$ .

Show answer

D. If $Q$ weighs 100, $P$ weighs 160. The difference 60 is now compared with 160: $60 \div 160 = 37.5%$ .

Question 7 · Modelled on 2013 P2 Q10 — the gain and the loss are different percentages, so the two costs must be found separately

Mandy sells two phones for $$3600$ each. She gains $20%$ on one and loses $25%$ on the other. After the two transactions, Mandy

gains $$180$ .
has no gain and no loss.
loses $$180$ .
loses $$600$ .

Show answer

D. The costs are $$3600 \div 1.2 = $3000$ and $$3600 \div 0.75 = $4800$ . Total cost $$7800$ against total sales $$7200$ is a loss of $$600$ .

Question 8 · Modelled on 2022 P1 Q5 — set as multiple-choice with the marked price given; the cost is asked

The marked price of a chair is $$750$ . The chair is sold at a discount of $20%$ on its marked price and the percentage profit is $25%$ . Find the cost of the chair.

$$450$
$$480$
$$562.5$
$$600$

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B. Selling price $= $750 \times 0.8 = $600$ , and cost $= $600 \div 1.25 = $480$ . Taking $25%$ off $$600$ gives $$450$ , which treats the profit as a percentage of the selling price.

Question 9 · Modelled on 2012 P2 Q8 — new groups and percentages; the simple average of the two percentages is a distractor

In a club, $40%$ of the members are adults. If $30%$ of the adult members and $55%$ of the other members are female, then the percentage of female members in the club is

$42.5%$ .
$45%$ .
$57.5%$ .
$85%$ .

Show answer

B. $40% \times 30% + 60% \times 55% = 12% + 33% = 45%$ . The plain average $42.5%$ would only be right if the two groups were the same size.

Question 10 · New sub-type: depreciation — no direct past-paper model; the syllabus pairs depreciation with compound interest

The value of a machine is $$80 000$ . If its value depreciates by $15%$ each year, find the value of the machine after 3 years.

$$41 760$
$$44 000$
$$49 130$
$$57 800$

Show answer

C. $$80 000 (0.85)^{3} = $49 130$ . Taking off $3 \times 15% = 45%$ at once gives $$44 000$ , which is too low.

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

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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