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Ratio, proportion and rates of change practice problems GCSE Maths, Topic 3

Written by STEM-Tutor's tutors · Updated October 2026 · 8 questions and 1 exam-style question

Sharing in a ratio, direct and inverse proportion, recipes and best buys, compound interest and depreciation, speed and density. Try each question before you look: use the hint if you are stuck, then reveal the worked solution one step at a time.

On this page
  1. Key equations
  2. Warm-up questions
  3. Exam-style questions
  4. Exam question practice
  5. Common mistakes
  6. Keep going

Key equations for ratio, proportion and rates of change

speed = distance ÷ timecompound measure
density = mass ÷ volumecompound measure
P(1 + r/100)ncompound interest

A formulae sheet is provided in the 2025, 2026 and 2027 GCSE Maths exams. Answers within 2.5% are marked correct, and you can type fractions such as 23/20. Every topic, Foundation and Higher, is in our GCSE Maths topic list.

Warm-up questions

Quick checks on the core ideas. If these feel easy, go straight to the exam-style questions.

Q1Warm-up
Share £60 in the ratio 2 : 3. What is the larger share?
£

Hint

Find the value of one part first.

Worked solution
  1. 2 + 3 = 5 parts, so 1 part = £12.
  2. Larger share = 3 × 12 = 36, so £36.
Q2Warm-up
A train travels 150 km in 2.5 hours. Work out its average speed.
km/h

Hint

Speed = distance ÷ time.

Worked solution
  1. 150 ÷ 2.5 = 60 km/h.
Q3Warm-up
y is directly proportional to x. When x = 3, y = 12. What is y when x = 5?

Hint

Find the multiplier k in y = kx.

Worked solution
  1. 12 = 3k, so k = 4.
  2. When x = 5, y = 20: B.

Exam-style questions

Questions at the level of the GCSE Maths exam. The ones marked Challenge combine more than one idea.

Q4Exam-style
A recipe uses 250 g of flour for 10 biscuits. How much flour is needed for 24 biscuits?
g

Hint

Find the flour for one biscuit, then scale up.

Worked solution
  1. 250 ÷ 10 = 25 g per biscuit.
  2. 25 × 24 = 600 g.
Q5Exam-style
£2000 is invested at 3% compound interest a year. How much is it worth after 4 years, to the nearest penny?
£

Hint

Multiply by 1.03 once for each year.

Worked solution
  1. 2000 × 1.034 = 2000 × 1.12551.
  2. = 2251.02, so £2251.02.
Q6Exam-style
6 workers take 10 days to build a wall. How long would 4 workers take, working at the same rate?
days

Hint

Fewer workers take longer: this is inverse proportion.

Worked solution
  1. Total work = 6 × 10 = 60 worker-days.
  2. 60 ÷ 4 = 15 days.
Q7Exam-style
A metal block has a mass of 540 g and a volume of 200 cm³. Work out its density.
g/cm³

Hint

Density = mass ÷ volume.

Worked solution
  1. 540 ÷ 200 = 2.7 g/cm³.
Q8ChallengeHigher
a : b = 3 : 4 and b : c = 2 : 5. If a = 12, find c.

Hint

Make the b parts match: write b : c as 4 : 10.

Worked solution
  1. b : c = 2 : 5 = 4 : 10, so a : b : c = 3 : 4 : 10.
  2. a = 12 means 1 part = 4, so c = 10 × 4 = 40.

Exam question practice

One original exam-style question in the style of a GCSE paper. Answer it in full, with working, before you open the mark scheme: most marks are for method, so show every step.

Exam-style question style · 6 points · about 6 minutes

A car costs £15 000. Its value falls by 12% each year.

  1. (a) Work out its value after 1 year.
  2. (b) Work out its value after 3 years.
  3. (c) Work out the total percentage decrease over the 3 years, to 1 decimal place.

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

15 000 × 0.88 = £13 200.

Part (b)

15 000 × 0.883 = £10 222.08.

Part (c)

0.883 = 0.681472, so the value has fallen by 31.9%.

Your mark: 0 of 6

Common mistakes in ratio, proportion and rates of change

Keep going

Revise the ideas behind these questions:

Then try real exam questions: GCSE Maths past papers, with official scoring guidelines. · All GCSE Maths units