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Cambridge IGCSE Maths (0580) · Topic 1: Number · 1.11

Cambridge IGCSE Maths 0580 Ratio and Proportion Questions

Ratio and Proportion questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise ratio and proportion →Ratio and Proportion notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Ratio and Proportion questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

Divide $\(96\) between Ana and Ben in the ratio \(5 : 3\). How much does each get?

Show the worked answer
  1. Total parts: \(5 + 3 = 8\). One part: \(96 \div 8 = 12\).
  2. Ana: \(5 \times 12 = 60\). Ben: \(3 \times 12 = 36\).

Answer: Ana $\(60\), Ben $\(36\)

Question 2 Core non-calculator · easy

Write each ratio in its simplest form.
(a) \(45 : 60\)
(b) \(2.5\) kg \(: 750\) g

Show the worked answer
  1. (a) Divide both by \(15\): \(3 : 4\).
  2. (b) Same units: \(2500 : 750\). Divide both by \(250\): \(10 : 3\).

Answer: (a) \(3 : 4\) (b) \(10 : 3\)

Question 3 Core calculator · easy · 2 marks

A recipe for 6 people uses 450 g of rice. How much rice is needed for 10 people?

Show the answer and mark scheme
  • M1 450 ÷ 6 × 10 oe
  • A1 750

Answer: \(750\) g

Question 4 Core non-calculator · medium

A recipe for \(6\) people uses \(450\) g of flour.
How much flour is needed for \(10\) people?

Show the worked answer
  1. For \(1\) person: \(450 \div 6 = 75\) g.
  2. For \(10\) people: \(75 \times 10 = 750\) g.

Answer: \(750\) g

Question 5 Core non-calculator · medium

In a club, the ratio of boys to girls is \(5 : 7\). There are \(20\) more girls than boys.
How many people are in the club?

Show the worked answer
  1. The difference is \(7 - 5 = 2\) parts, so \(2\) parts \(= 20\) and \(1\) part \(= 10\).
  2. Total: \(12\) parts \(= 120\).

Answer: \(120\)

Question 6 Core calculator · medium

A map has a scale of \(1 : 25\,000\). Two villages are \(6.4\) cm apart on the map.
Find the real distance between them in kilometres.

Show the worked answer
  1. Real distance \(= 6.4 \times 25\,000 = 160\,000\) cm.
  2. \(160\,000\) cm \(= 1600\) m \(= 1.6\) km.

Answer: \(1.6\) km

Question 7 Core non-calculator · medium

\(x : y = 2 : 3\) and \(y : z = 4 : 5\).
Find \(x : y : z\) in its simplest form.

Show the worked answer
  1. Make the \(y\) parts the same: \(2 : 3 = 8 : 12\) and \(4 : 5 = 12 : 15\).
  2. So \(x : y : z = 8 : 12 : 15\).

Answer: \(8 : 12 : 15\)

Question 8 Core non-calculator · medium · 2 marks

The ratio of boys to girls in a club is \(3 : 5\). There are 35 girls. How many students are in the club altogether?

Show the answer and mark scheme
  • M1 35 ÷ 5 = 7
  • A1 56

Answer: \(56\)

Question 9 Core calculator · medium · 2 marks

Blue paint and white paint are mixed in the ratio \(2 : 7\). Ali uses 1.8 litres of blue paint. How many litres of paint does he make altogether?

Show the answer and mark scheme
  • M1 1.8 ÷ 2 (= 0.9)
  • A1 8.1

Answer: \(8.1\) litres

Question 10 Core non-calculator · hard

A bag holds red and blue counters in the ratio \(3 : 5\). After \(18\) red counters are added, the ratio of red to blue is \(3 : 2\).
How many counters were in the bag at the start?

Show the worked answer
  1. Start: \(3k\) red and \(5k\) blue.
  2. \(\frac{3k + 18}{5k} = \frac{3}{2}\), so \(2(3k + 18) = 15k\), \(6k + 36 = 15k\), \(k = 4\).
  3. At the start: \(12\) red and \(20\) blue, \(32\) counters.

Answer: \(32\)

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test ratio and proportion?

Ratio and Proportion is on both tiers (syllabus 1.11), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more ratio and proportion questions?

In the 0580 practice for topic 1 (Number), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More number questions