GCSE Maths Practice: sharing-in-a-ratio

Question 10 of 10

This question checks your ability to match a named person to the correct part of a ratio.

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\( \begin{array}{l}\text{£96 is shared between James and Olivia in the ratio } 3:5. \\ \text{How much does Olivia receive?}\end{array} \)

Choose one option:

After calculating both shares, check that they add up to the original total.

Finding a Named Person’s Share in a Two-Part Ratio (GCSE Higher)

At GCSE Higher level, ratio questions often assess how well you interpret the wording as well as how accurately you calculate. When a question asks for a named person’s share, such as Olivia’s, you must match the name to the correct number in the ratio before doing any calculations.

Understanding What the Ratio Represents

A ratio like 3:5 shows how a total is divided into equal parts. The first number refers to the first person named, and the second number refers to the second person named. These numbers are not the values themselves; they tell you how many equal parts each person receives.

Why Order Matters

In name-based ratio questions, errors often occur when students calculate correctly but attach the result to the wrong person. Always read the order carefully: the first name matches the first ratio number, and the second name matches the second ratio number.

Efficient Higher-Tier Method

  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. Identify the ratio number that belongs to the named person.
  4. Multiply the unit value by that ratio number.

This method is consistent across all sharing-in-a-ratio questions, whether the numbers are simple or more complex.

Worked Example 1

£84 is shared between Alex and Sam in the ratio 2:5. How much does Sam receive?

  • Total parts = 2 + 5 = 7
  • One part = £84 ÷ 7 = £12
  • Sam receives 5 × £12 = £60

Worked Example 2

72 points are divided between Team A and Team B in the ratio 3:1. How many points does Team B receive?

  • Total parts = 3 + 1 = 4
  • One part = 72 ÷ 4 = 18
  • Team B receives 1 × 18 = 18 points

Common Higher-Tier Errors

  • Swapping the shares: Always match names to ratio numbers.
  • Dividing by one ratio number: You must divide by the sum of the parts.
  • Skipping the final check: Both shares should add back to the total.

Exam Technique

Underline the name you are asked about and circle it in the ratio before calculating. This simple habit prevents many careless mistakes.

Real-Life Applications

Name-based ratios are common in situations such as profit sharing between partners, dividing wages for joint work, and allocating resources between departments. Accuracy is essential to ensure fairness.

Frequently Asked Questions

Q: Can I simplify the ratio first?
Yes. Simplifying ratios makes calculations easier but does not change which person gets which share.

Q: Does the second person always receive the larger share?
No. The size of the share depends on the ratio values, not the position.

Study Tip

Write the ratio underneath the names before starting your working. Clear organisation leads to fewer errors.

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