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 (Intermediate, 10 Questions)

2026-11-06

Tutor Prep Guide · S2 Mathematics

Ten intermediate items on reverse percentage, finding the original value, three-term and linked ratios, successive percentage changes and scale conversion, each with an answer and a note.

Quick answer Answers in order: 360 dollars, 120%, 60, 40, 150, 400, 9 : 12 : 10, 105.6 g, 19%, 3 km. For reverse questions write original x multiplier = new value, then divide.

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 30 minutes
Difficulty mix	Intermediate 10
Chapter	Chapter: S2 Maths: Percentages and Ratio
Level	S2

02 Questions (10 items)

IntermediateAfter a 15% rise an item sells for 414 dollars. Find the original price.
IntermediateCost is 60 dollars and selling price is 72 dollars. Selling price is what percentage of cost?
IntermediateA number becomes 78 after a 30% increase. Find the number.
IntermediateIncrease 40 by 25% and then decrease the result by 20%. What is the final value?
IntermediateThree numbers are in the ratio 2 : 3 : 5 and add up to 300. Find the largest.
IntermediateDivide 720 in the ratio 5 : 3 : 1. Find the largest share.
IntermediateGiven a : b = 3 : 4 and b : c = 6 : 5, find a : b : c.
IntermediateA 480 g can of beans is 22% protein. Find the mass of protein.
IntermediateAn item is reduced by 10% twice. Find the total percentage decrease.
IntermediateA map has a scale of 1 : 50000. What real distance does 6 cm represent?

03 Answers and one-line notes

#	Answer	One-line note
1	360 dollars	Original price x 1.15 = 414, so the original price is 414 / 1.15 = 360 dollars.
2	120%	72 / 60 = 1.2, which is 120%.
3	60	Number x 1.3 = 78, so the number is 78 / 1.3 = 60.
4	40	40 x 1.25 = 50 and 50 x 0.8 = 40, which is back to the start.
5	150	There are 10 parts of 30 each, and the largest takes 5 parts, giving 150.
6	400	There are 9 parts of 80 each, and the largest share is 5 parts, or 400.
7	9 : 12 : 10	Take b as 12, the L.C.M. of 4 and 6, so a becomes 9 and c becomes 10.
8	105.6 g	480 x 0.22 = 105.6 g.
9	19%	0.9 x 0.9 = 0.81, so the final price is 81% of the original and the total cut is 19%.
10	3 km	6 x 50000 = 300000 cm, which is 3 km.

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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