Why do percentages and ratio matter in S2?

S2 applies percentages to discounts, profit, growth and interest, and ratio to sharing and map scales; the two often appear in one question and underpin school tests and the DSE.

Why find the value of one part first?

In ratio sharing, find the total number of parts, then the value of one part, then multiply by each share, so every step can be checked.

S2 Maths: Percentages and Ratio (Challenge, 10 Questions)

2026-11-06

Tutor Prep Guide · S2 Mathematics

Ten challenge items mixing percentages with ratio: marked price and profit percentage, mixing two syrups, linked ratios, simple interest, successive changes, two map scales and two-step percentage work, all with answers and notes.

Quick answer Answers in order: 12%, 63, 240, 30%, 16%, 63, 400 dollars, 96%, 2 cm, 6. In mixed items decide first which quantity is the 100%, then choose multiply or divide.

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 35 minutes
Difficulty mix	Challenge 10
Chapter	Chapter: S2 Maths: Percentages and Ratio
Level	S2

02 Questions (10 items)

ChallengeCost is 480 dollars. The marked price is 40% above cost and the item is sold at 20% off the marked price. Find the profit percentage.
ChallengeBoys : girls = 5 : 7 and there are 45 boys. How many girls are there?
Challenge35% of a number is 84. Find the number.
ChallengeA value rises from 25 to 32.5. Find the percentage increase.
Challenge40 g of syrup is 25% sugar and 60 g of syrup is 10% sugar. Find the sugar percentage of the mixture.
ChallengeTwo numbers are in the ratio 4 : 7 and differ by 27. Find the larger number.
Challenge5000 dollars is deposited at 4% simple interest per year for 2 years. Find the interest.
ChallengeAn item is raised by 20% and then cut by 20%. What percentage of the original price is left?
ChallengeMap A has a scale of 1 : 20000 and map B 1 : 50000. A road is 5 cm on map A. Find its length on map B.
ChallengeA class of 40 is 60% girls, and 25% of the girls wear glasses. How many girls wear glasses?

03 Answers and one-line notes

#	Answer	One-line note
1	12%	Marked price 672, selling price 537.6, profit 57.6, and 57.6 / 480 = 12%.
2	63	45 / 5 = 9 per part, so 7 parts give 63 girls.
3	240	Number x 0.35 = 84, so the number is 84 / 0.35 = 240.
4	30%	The rise is 7.5, and 7.5 / 25 = 0.3, which is 30%.
5	16%	The sugar totals 10 + 6 = 16 g in 100 g of syrup, so the mixture is 16%.
6	63	The difference is 3 parts equal to 27, so one part is 9 and the larger number is 63.
7	400 dollars	Simple interest = 5000 x 0.04 x 2 = 400 dollars.
8	96%	1.2 x 0.8 = 0.96, which is 96% of the original price.
9	2 cm	The real length is 5 x 20000 = 100000 cm, so on map B it is 100000 / 50000 = 2 cm.
10	6	Girls number 40 x 0.6 = 24, and 24 x 0.25 = 6 wear glasses.

04 What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.