Inverse Quantity Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Inverse Quantity.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A relationship where one quantity increases as another decreases, with constant product.

More workers = less time to finish. Double the workers, halve the time.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Inverse relationship: xy = k, so if x doubles, y halves.

Common stuck point: Confusing inverse proportion (xy = k) with subtraction—'inverse' here means product is constant, not difference.

Sense of Study hint: Multiply the two quantities together for each pair of values. If the product is always the same constant, the relationship is inverse.

Worked Examples

Example 1

easy
If 5 workers can complete a job in 12 days, how many days will it take 15 workers (assuming equal work rates)?

Solution

  1. 1
    Total work = 5 \times 12 = 60 worker-days.
  2. 2
    With 15 workers: days = \dfrac{60}{15} = 4 days.
  3. 3
    Alternatively: workers and days are inversely proportional, so 5 \times 12 = 15 \times d, giving d = 4.

Answer

It will take 4 days.
When two quantities are inversely proportional, their product is constant. More workers means fewer days, and the product (total worker-days) stays the same. The relationship is w \times d = k, not w/d = k.

Example 2

medium
The pressure P of a gas varies inversely with its volume V at constant temperature (Boyle's Law). If P = 200 kPa when V = 3 L, find P when V = 5 L.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
At 60 km/h a trip takes 4 hours. How long does the same trip take at 80 km/h?

Example 2

medium
Variables x and y are inversely proportional. When x = 4, y = 9. Find y when x = 12, and find x when y = 6.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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