GCSE Maths Practice: sharing-in-a-ratio

Question 1 of 10

This question tests your ability to share a total accurately using a given ratio.

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\( \begin{array}{l}\text{Which of the following correctly share £120 in the ratio } 3:5\text{?}\end{array} \)

Choose one option:

Check both the ratio and the total when selecting an answer.

Sharing an Amount in a Ratio (GCSE Higher)

At GCSE Higher level, ratio questions are designed to test accuracy, efficiency, and careful interpretation rather than just following a memorised method. Sharing an amount in a given ratio remains a core skill, but questions may appear in multiple-choice form or be embedded within longer problems.

Key Idea Behind Ratio Sharing

A ratio such as 3:5 tells us how two quantities compare. When sharing a total, this means the total amount is divided into equal parts based on the sum of the ratio values. The actual size of each share depends entirely on the total.

Efficient Method for Higher Tier

  1. Add the numbers in the ratio to find the total number of parts.
  2. Divide the total amount by this number to find the value of one part.
  3. Multiply the value of one part by each ratio number.

At Higher level, you are expected to carry out these steps quickly and accurately, often without writing every stage in full.

Worked Example 1

£96 is shared in the ratio 2:6. What are the two shares?

  • Total parts = 2 + 6 = 8
  • One part = £96 ÷ 8 = £12
  • Shares = £24 and £72

Worked Example 2

150 points are divided between two teams in the ratio 4:1. How many points does each team receive?

  • Total parts = 4 + 1 = 5
  • One part = 150 ÷ 5 = 30
  • Shares = 120 points and 30 points

Common Higher-Tier Pitfalls

  • Incorrect total parts: Adding the ratio incorrectly leads to every answer being wrong.
  • False symmetry: Equal-looking options (e.g. £60 and £60) may distract but only work for 1:1 ratios.
  • Not checking totals: Each option should add back to the original amount.

Exam Strategy for Multiple-Choice Questions

In multiple-choice ratio questions, you can often eliminate incorrect options quickly by checking whether the two values add up to the total. Then check whether the remaining options follow the correct ratio.

Real-Life Applications

Ratio sharing is used in business profit splits, budgeting, recipe scaling, and dividing workloads. At higher levels, ratios may also be combined with percentages or algebra.

Frequently Asked Questions

Q: Can the ratio be simplified first?
Yes. Simplifying ratios often makes calculations quicker and reduces errors.

Q: Is there always only one correct answer?
Yes. Only one option will both match the ratio and add to the correct total.

Study Tip

In exams, quickly divide the total by the sum of the ratio parts before looking at the answer options. This keeps your thinking structured and efficient.

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