GCSE Maths Practice: sharing-in-a-ratio

Question 7 of 10

This question tests your ability to match a specific person to the correct part of a three-part ratio.

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\( \begin{array}{l}\text{£250 is divided between three people in the ratio } 1:4:5. \\ \text{How much does the second person receive?}\end{array} \)

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 often assess how accurately you interpret the wording as well as how confidently you calculate. When a question asks for the second person’s share, you must pay close attention to the order of the ratio and the order of the people listed. This type of question is designed to catch students who calculate correctly but match the wrong part of the ratio.

Understanding Position in a Ratio

A ratio such as 1:4:5 shows how a total is divided between three people. 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 represent how many equal parts each person receives, not the actual amounts.

Why Order Matters

In three-part ratios, it is easy to accidentally choose the smallest or largest share instead of the correct one. When a question specifies a position, such as the second person, you must match that position to the correct number in the ratio before calculating.

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 the ratio number that corresponds to the second person.
  4. Multiply the value of one part by that number.

Worked Example 1

£180 is shared between three people in the ratio 2:3:5. How much does the second person receive?

  • Total parts = 2 + 3 + 5 = 10
  • One part = £180 ÷ 10 = £18
  • Second person receives 3 × £18 = £54

Worked Example 2

240 points are divided between three teams in the ratio 4:1:3. How many points does the second team receive?

  • Total parts = 4 + 1 + 3 = 8
  • One part = 240 ÷ 8 = 30
  • Second team receives 1 × 30 = 30 points

Common Higher-Tier Errors

  • Ignoring the order: Always match the person’s position to the correct ratio number.
  • Using the wrong multiplier: The second person does not always receive the smallest or largest share.
  • Skipping the unit value: You must always calculate one part first.

Exam Technique

Underline the phrase second person and draw arrows from the names to the ratio numbers before starting calculations. This small step prevents most position-based errors.

Real-Life Applications

Position-based ratios appear in situations such as profit sharing between partners, distributing tasks based on role, or allocating resources according to responsibility. Understanding how order affects ratios is essential for accuracy.

Frequently Asked Questions

Q: Can the ratio be simplified first?
Yes. Simplifying ratios makes calculations easier but does not change which share belongs to which person.

Q: Is the second person always the middle share?
Not necessarily. The size of the share depends on the ratio, not its position.

Study Tip

Write the ratio underneath the people’s names before calculating. This keeps your working organised and avoids mixing up shares.

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