GCSE Maths Practice: inverse-proportion

Question 4 of 10

This question tests inverse proportion using people and time.

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\( \begin{array}{l}\text{8 people complete a job in 18 days.} \\ \text{How many days would 12 people take to complete the same job?}\end{array} \)

Choose one option:

Inverse Proportion with People and Time

This question is about inverse proportion, a GCSE Maths topic that often appears in problems involving people, machines, or time. In inverse proportion, one quantity increases while the other decreases, but the overall amount of work stays the same.

In work-based problems, the job being completed does not change. This means that whether fewer people take longer or more people take less time, the total work remains constant.

The Key Rule

For questions involving people and days, the rule is:

number of people × number of days = constant

This rule allows you to set up a simple equation and solve the problem efficiently.

Step-by-Step Method

  1. Identify the two linked quantities (people and days).
  2. Multiply the given values to find the total work.
  3. Keep this total the same for the new situation.
  4. Solve the equation to find the missing value.

Writing your working clearly helps you gain full marks in GCSE exams.

Worked Example (Different Numbers)

Example: 6 people take 20 days to complete a task. How many days would 10 people take?

  • Total work = 6 × 20 = 120
  • Let the new time be t
  • 10 × t = 120
  • t = 12 days

This example shows that increasing the number of people reduces the time needed.

Another Example Using More Workers

Example: 5 workers complete a job in 24 days. How long would it take 15 workers?

  • Total work = 5 × 24 = 120
  • 15 × t = 120
  • t = 8 days

Tripling the number of workers reduces the time taken.

Common Mistakes to Avoid

  • Using direct proportion instead of inverse proportion.
  • Adding or subtracting instead of multiplying.
  • Assuming more people means more days.
  • Forgetting that the total work must stay the same.

Real-Life Applications

Inverse proportion appears in many real-life situations. For example, if more people help prepare an event, the setup time is reduced. In workplaces, adding staff to a task usually shortens the completion time.

Frequently Asked Questions

How can I tell if a question is inverse proportion?
If increasing one quantity causes the other to decrease for the same task, the relationship is inverse.

Do these questions always involve time?
Often, but they can also involve speed, machines, or rates.

Study Tip

Before calculating, ask yourself whether the answer should be larger or smaller. This quick sense check can help you avoid common GCSE exam errors.

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