GCSE Maths Practice: inverse-proportion

Question 3 of 10

This question tests inverse proportion using workers and days.

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\( \begin{array}{l}\text{6 workers take 8 days to complete a job.} \\ \text{How many days would 12 workers take to complete the same job?}\end{array} \)

Choose one option:

Inverse Proportion with Workers and Time

This question focuses on inverse proportion, a key GCSE Maths topic that often appears in problems involving people, machines, or time. In inverse proportion, when one quantity increases, the other decreases so that the total outcome remains the same.

In work-based problems, the important idea is that the total amount of work stays constant. Whether fewer workers take longer or more workers take less time, the job being completed does not change.

The Core Relationship

For questions involving workers and days, we use the rule:

number of workers × number of days = constant

This relationship helps you quickly recognise inverse proportion questions and choose the correct method.

Step-by-Step Method

  1. Identify the two linked quantities (workers and days).
  2. Calculate the total work using the first situation.
  3. Keep this total the same for the new situation.
  4. Form a simple equation and solve it.

Showing these steps clearly helps secure marks in GCSE exams.

Worked Example (Different Numbers)

Example: 5 workers take 12 days to complete a job. How long would it take 10 workers?

  • Total work = 5 × 12 = 60
  • Let the new time be t
  • 10 × t = 60
  • t = 6 days

This example shows that doubling the number of workers halves the time.

Another Example with More Workers

Example: 4 builders take 15 days to complete a task. How long would 12 builders take?

  • Total work = 4 × 15 = 60
  • 12 × t = 60
  • t = 5 days

As the workforce increases, the time required decreases.

Common Mistakes to Avoid

  • Using direct proportion instead of inverse proportion.
  • Adding or subtracting values instead of multiplying.
  • Assuming more workers means more time.
  • Forgetting to keep the total work the same.

Real-Life Applications

Inverse proportion is common in everyday life. For example, hiring more people to move furniture usually means the job is finished faster. In construction, increasing the number of workers often reduces the number of days needed to complete a project.

Frequently Asked Questions

How do I know this is inverse proportion?
If more workers lead to fewer days for the same task, the relationship is inverse.

Should I always multiply first?
Yes. Multiplying helps you find the total work, which must stay constant.

Study Tip

Before solving, ask yourself whether the time should increase or decrease. This quick check can help you avoid common GCSE exam errors.

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