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GCSE Maths / Edexcel

Finding missing amounts from a ratio

Use a known part of a ratio to find one part, another amount, or the total amount.

Ratio, Proportion and RatesFoundation and HigherGrades 4 to 6Focused skill

Curriculum path: GCSE Maths > Edexcel > Ratio, Proportion and Rates > Missing amounts from a ratio

Pearson Edexcel GCSE Maths ratio R5 and R8: use ratios to find quantities when another quantity is known.

Practise this topicUpload your answerAsk AI to explain thisTry exam-style questions
Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Some ratio questions do not give the total. Instead, they give one share and ask for another share or the total.

Match the known amount to its ratio part first. This is the most important line of working.

Divide the known amount by its ratio part to find one part.

Multiply one part by the ratio part you need, or by the total parts if the question asks for the total.

Read the question carefully: it may ask for the other amount, the difference, or the total.

Key ruleKnown amount / matching ratio part = one part.

Worked examples

Find another amount

Boys:girls = 3:5. There are 18 boys. How many girls are there?

  1. 3 parts = 18 boys.
  2. One part = 18 / 3 = 6.
  3. Girls = 5 parts = 5 x 6.

Answer: 30 girls

Find the total

Red:blue = 4:7. There are 28 blue counters. How many counters are there altogether?

  1. 7 parts = 28.
  2. One part = 4.
  3. Total parts = 4 + 7 = 11.
  4. Total = 11 x 4.

Answer: 44 counters

Find a difference

A:B = 2:9. B is 63. How much more is B than A?

  1. 9 parts = 63.
  2. One part = 7.
  3. A = 14 and B = 63.
  4. Difference = 63 - 14.

Answer: 49

Common mistakes

  • Matching the known amount to the wrong ratio part.
  • Adding the ratio parts before deciding whether the known amount is a share or the total.
  • Finding the other amount when the question asks for the total.
  • Forgetting units in context questions.

Quick exercise

Try these before moving to the exam-style questions.

  1. Red:blue = 2:5. Red is 14. Find blue.
  2. Boys:girls = 4:3. Girls are 21. Find boys.
  3. A:B = 5:6. A is 40. Find the total.
  4. Cats:dogs = 3:8. Dogs are 56. Find cats.
  5. Small:large = 2:7. Large is 49. Find the difference.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator3 marks

Pens:pencils = 4:7. There are 20 pens. Work out the number of pencils.

missing ratio amountone partfoundation ratio
Standard exam styleFoundation and HigherEither4 marks

The ratio of adults to children at a concert is 5:8. There are 96 children. Work out the total number of people at the concert.

ratio totalcontext problemmethod marks
ChallengeFoundation and HigherEither5 marks

In a school, the ratio of Year 10 students to Year 11 students is 7:9. There are 48 more Year 11 students than Year 10 students. Find the number of Year 11 students.

ratio differencereverse ratiohigher reasoning