IGCSE Mathematics: Ratio and Proportion Practice Questions
To share a quantity in a given ratio, add the parts, divide the total by that number to find one part, then multiply. In direct proportion one quantity is a constant multiple of the other, and in inverse proportion their product is constant.
Topic 1.11 of Cambridge IGCSE Mathematics 0580 runs through the whole paper, appearing in geometry, statistics and problem solving as well as in number. Finding the value of one part, or the constant of proportionality, is the step that every question depends on. The questions below build that habit.
What you need to know for Ratio and Proportion
- Sharing in a ratioAdd the parts to find the total number of parts, divide the quantity by that total to find one part, then multiply by each share.
- Simplifying a ratioDivide every part by their highest common factor. Ratios must be in the same units before simplifying.
- Direct proportiony is directly proportional to x means y = kx for a constant k. If y is proportional to the square of x, then y = kx2.
- Inverse proportiony is inversely proportional to x means y = k divided by x, so the product xy is constant. Doubling x halves y.
- Finding kSubstitute the given pair of values into the equation to find the constant, then rewrite the equation and use it for the second pair.
- Map scalesA scale of 1 to 25000 means 1 cm on the map represents 25000 cm on the ground, which is 250 m or 0.25 km.
IGCSE Mathematics Ratio and Proportion questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
Share RM840 between three people in the ratio 3 : 4 : 5.
Show the worked answer
- Add the parts: 3 + 4 + 5 = 12 parts in total.
- Find the value of one part: RM840 divided by 12 = RM70.
- Multiply each share: 3 x 70 = RM210, 4 x 70 = RM280, and 5 x 70 = RM350.
- Check: 210 + 280 + 350 = RM840, which matches the original amount.
y is directly proportional to the square of x. When x = 3, y = 18. Find the value of y when x = 5.
Show the worked answer
- Write the relationship as an equation: y = kx2.
- Substitute the known pair: 18 = k x 32 = 9k, so k = 2.
- The equation is therefore y = 2x2.
- Substitute x = 5: y = 2 x 25 = 50.
The time t taken to complete a job is inversely proportional to the number of workers n. When 4 workers are used the job takes 6 hours. Find how long it takes with 3 workers.
Show the worked answer
- Write the relationship: t = k divided by n.
- Substitute the known pair: 6 = k divided by 4, so k = 24.
- The equation is therefore t = 24 divided by n.
- Substitute n = 3: t = 24 divided by 3 = 8 hours. This is sensible, since fewer workers should take longer.
On a map with scale 1 : 25000, two towns are 6 cm apart. Calculate the actual distance between them in kilometres.
Show the worked answer
- A scale of 1 to 25000 means 1 cm on the map represents 25000 cm on the ground.
- 6 cm on the map therefore represents 6 x 25000 = 150000 cm.
- Convert to metres by dividing by 100: 150000 divided by 100 = 1500 m.
- Convert to kilometres by dividing by 1000: 1500 divided by 1000 = 1.5 km.
Common mistakes in this topic
- Dividing by the number of shares instead of the total number of parts.
- Simplifying a ratio without first converting to the same units.
- Using direct proportion reasoning on an inverse proportion problem.
- Forgetting to square or cube x when the proportion involves a power.
- Losing a factor of 10 in map scale unit conversions.
Exam tips
- Always find the value of one part first and write it down. It is a method mark and it makes every share a single multiplication.
- For proportion questions, write the equation with k, find k, then rewrite the full equation before substituting.
- Sense check inverse proportion answers: if one quantity goes down, the other must go up.
- Check that your shares add back to the original total. It takes seconds and catches arithmetic slips.
- For map scales, convert centimetres to metres then metres to kilometres, one step at a time.
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Ratio and Proportion FAQs
How do I share an amount in a ratio?
Add the parts of the ratio to find the total number of parts, divide the amount by that total to find the value of one part, then multiply that value by each part of the ratio. Check by adding the shares back together to confirm they give the original amount.
What is the difference between direct and inverse proportion?
In direct proportion, y equals k multiplied by x, so as one quantity increases the other increases in the same ratio. In inverse proportion, y equals k divided by x, so as one increases the other decreases and their product stays constant.
How do I find the constant of proportionality?
Write the relationship as an equation with k, substitute the pair of values you are given, and solve for k. Then rewrite the complete equation with that value of k and use it to find the unknown quantity in the second part of the question.
How do I convert a map scale into real distances?
Multiply the map distance by the scale factor to get the real distance in the same unit. For a 1 to 25000 scale, 6 cm on the map represents 150000 cm on the ground. Divide by 100 for metres, then by 1000 for kilometres.
Continue through the IGCSE Mathematics syllabus
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.