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Direct & inverse proportion practice questions with answers

Higher · Grade 5

A second set of direct & inverse proportion questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

2 workers take 10 hours to finish a job. How many hours do 4 workers take?

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Answer: 5

  1. Find total worker-hours: 2 × 10 = 20.
  2. Divide by 4 workers: 20 / 4 = 5.
  • Method (1): Find total worker-hours: 2 × 10 = 20.
  • Accuracy (1): Divide by 4 workers: 20 / 4 = 5.

Question 2 Easy

8 workers take 3 hours to finish a job. How many hours do 6 workers take?

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Answer: 4

  1. Find total worker-hours: 8 × 3 = 24.
  2. Divide by 6 workers: 24 / 6 = 4.
  • Method (1): Find total worker-hours: 8 × 3 = 24.
  • Accuracy (1): Divide by 6 workers: 24 / 6 = 4.

Question 3 Medium

y is directly proportional to x. y = 9 when x = 3. Find y when x = 1.

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Answer: 3

  1. Find constant: k = 9 / 3 = 3.
  2. Calculate y = 3 × 1 = 3.
  • Method (1): Find constant: k = 9 / 3 = 3.
  • Accuracy (1): Calculate y = 3 × 1 = 3.

Question 4 Medium

y is directly proportional to x. y = 4 when x = 2. Find y when x = 9.

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Answer: 18

  1. Find constant: k = 4 / 2 = 2.
  2. Calculate y = 2 × 9 = 18.
  • Method (1): Find constant: k = 4 / 2 = 2.
  • Accuracy (1): Calculate y = 2 × 9 = 18.

Question 5 Hard

y is directly proportional to x. y = 15 when x = 5. Find the constant k.

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Answer: 3

  1. Direct proportion formula: k = y / x.
  2. Calculate k = 15 / 5 = 3.
  • Method (1): Direct proportion formula: k = y / x.
  • Accuracy (1): Calculate k = 15 / 5 = 3.

Question 6 Hard

y is inversely proportional to x. y = 6 when x = 4. Find the constant k.

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Answer: 24

  1. Inverse proportion formula: k = xy.
  2. Calculate k = 6 × 4 = 24.
  • Method (1): Inverse proportion formula: k = xy.
  • Accuracy (1): Calculate k = 6 × 4 = 24.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

y is inversely proportional to x. y = 15 when x = 2. Find y when x = 6.

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Answer: 5

  1. Find constant k: k = 15 × 2 = 30.
  2. Divide by new x: y = 30 / 6 = 5.
  • Method (1): Writes y = k/x, or 15 = k/2
  • Method (1): k = 30, so y = 30/x
  • Accuracy (1): 5

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

More workers sharing the same job means what for completion time?

  1. Less time
  2. More time
  3. Same time
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Less time Work is shared, so time decreases.

Check 2

4 workers take 6 hours. How long do 8 workers take?

  1. 3 hours
  2. 12 hours
  3. 8 hours
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3 hours 24 worker-hours shared by 8 is 3 hours.

Check 3

6 workers take 4 hours. How long do 3 workers take?

  1. 8 hours
  2. 2 hours
  3. 6 hours
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8 hours 24 worker-hours shared by 3 is 8 hours.

Check 4

y is directly proportional to x. y = 10 when x = 2. When x = 5, what is y?

  1. 25
  2. 15
  3. 20
Show answer

25 k = 5, so 5 × 5 = 25.

Check 5

y is directly proportional to x. y = 8 when x = 4. When x = 6, what is y?

  1. 12
  2. 10
  3. 16
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12 k = 2, so 2 × 6 = 12.

Check 6

y is inversely proportional to x. y = 12 when x = 3. When x = 4, what is y?

  1. 9
  2. 16
  3. 6
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9 xy = 36, so 36 / 4 = 9.

Check 7

y is inversely proportional to x. y = 20 when x = 2. When x = 5, what is y?

  1. 8
  2. 50
  3. 10
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8 xy = 40, so 40 / 5 = 8.

Check 8

y is directly proportional to x. y = 15 when x = 5. What is the constant k?

  1. 3
  2. 75
  3. 10
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3 k = 15 ÷ 5 = 3.

Check 9

y is inversely proportional to x. y = 6 when x = 4. What is the constant k?

  1. 24
  2. 1.5
  3. 10
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24 k = 6 × 4 = 24.

Check 10

Which equation represents direct proportion?

  1. y = kx
  2. y = k/x
  3. y = k + x
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y = kx Direct proportion has y proportional to x with multiplier k.

Check 11

Which equation represents inverse proportion?

  1. y = k/x
  2. y = kx
  3. y = x/k
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y = k/x Inverse proportion means the product xy is constant.

Check 12

How do you calculate total worker-hours?

  1. Multiply workers by hours
  2. Divide workers by hours
  3. Add workers and hours
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Multiply workers by hours Worker-hours is the product of team size and time.

Check 13

If x doubles and y doubles, what type of proportion is it?

  1. Direct
  2. Inverse
  3. Neither
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Direct Both variables scale by the same factor.

Check 14

If x doubles and y halves, what type of proportion is it?

  1. Inverse
  2. Direct
  3. Neither
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Inverse One doubles while the other halves, keeping xy constant.

Check 15

What should you find first in a proportion problem?

  1. The constant of proportionality k
  2. The final graph
  3. The average of x and y
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The constant of proportionality k Finding k allows you to evaluate any other pair.

Keep going with Direct & inverse proportion

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