GCSE Maths Practice: sharing-in-a-ratio

Question 9 of 10

This question tests your ability to correctly match a person’s position to the correct part of a three-part ratio.

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\( \begin{array}{l}\text{£315 is shared between three people in the ratio } 4:5:6. \\ \text{What does the second person receive?}\end{array} \)

Choose one option:

After finding all three shares, check that they add up to the original total.

Finding the Second Person’s Share in a Three-Part Ratio (GCSE Higher)

At GCSE Higher level, ratio questions are designed to test more than basic calculation. When a question asks for the second person’s share, you must correctly interpret the order of the ratio as well as apply the unit-value method accurately. Many mistakes occur not because the maths is difficult, but because the ratio is matched to the wrong person.

Understanding Order in Ratios

A ratio such as 4:5:6 shows how a total amount is divided between three people in a specific order. The first number refers to the first person, the second number refers to the second person, and the third number refers to the third person. The numbers themselves represent how many equal parts each person receives.

Why Position Matters

In three-part ratios, it is common for students to accidentally select the smallest or largest share instead of the share belonging to the person named. When the question specifies a position, such as the second person, you must focus on the correct ratio number before carrying out any calculations.

Efficient Higher-Tier Method

  1. Add all 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 which number in the ratio belongs to the second person.
  4. Multiply the value of one part by that number.

This structured approach keeps your working clear and avoids mixing up the shares.

Worked Example 1

£240 is shared between three people in the ratio 3:5:4. How much does the second person receive?

  • Total parts = 3 + 5 + 4 = 12
  • One part = £240 ÷ 12 = £20
  • Second person receives 5 × £20 = £100

Worked Example 2

180 points are divided between three teams in the ratio 2:6:1. How many points does the second team receive?

  • Total parts = 2 + 6 + 1 = 9
  • One part = 180 ÷ 9 = 20
  • Second team receives 6 × 20 = 120 points

Common Higher-Tier Errors

  • Ignoring the order: Always match people to the correct ratio number.
  • Using the wrong multiplier: The second person is not always the middle-sized share.
  • Skipping the unit value: You must always find one part first.

Exam Technique

Underline the phrase second person and write the ratio numbers underneath the names before calculating. This simple step prevents most position-based mistakes.

Real-Life Applications

Position-based ratios appear in profit sharing, workload distribution, budgeting between departments, and task allocation within teams. Understanding how order affects ratios ensures accuracy in real-world decision-making.

Frequently Asked Questions

Q: Can the ratio be simplified first?
Yes. Simplifying ratios can make calculations quicker but does not change which person receives which share.

Q: Does the second person always receive the middle amount?
No. The size of the share depends entirely on the ratio values.

Study Tip

Write the ratio clearly under the names before starting calculations. Clear organisation leads to fewer errors.

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