Lesson R10

R10 Direct and inverse proportion problems Quiz: AQA Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson R10, Direct and inverse proportion problems: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 3: Ratio, proportion and rates of change, written with Revision Ninja.

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The 20 questions

  1. y is directly proportional to x. When x = 4, y = 20. What is y when x = 7?

    • 28
    • 32
    • 35
    • 140

  2. y is inversely proportional to x. When x = 3, y = 8. What is y when x = 6?

    • 2
    • 4
    • 11
    • 16

  3. Which statement describes inverse proportion?

    • As x doubles, y halves.
    • As x doubles, y stays the same.
    • As x doubles, y doubles.
    • As x doubles, y increases by 2.

  4. What is the graph of a direct proportion relationship y = kx?

    • A straight line crossing the y-axis above zero
    • A straight line passing through the origin
    • A horizontal line at height k
    • A curve that never touches either axis

  5. What shape is the graph of y = k/x for positive k, drawn in the first quadrant?

    • A curve that passes through the origin and rises steadily
    • A curve that meets the y-axis at k and the x-axis at 1/k
    • A straight line that slopes downwards from the top left
    • A curve that approaches both axes but never touches them

  6. 5 workers take 12 days to build a wall. At the same rate, how many days would 8 workers take?

    • 7.5 days
    • 8.5 days
    • 19.2 days
    • 7.2 days

  7. 6 pens cost £4.50. At the same price per pen, what would 10 pens cost?

    • £7.50
    • £45.00
    • £7.20
    • £6.75

  8. If y is directly proportional to x and y = 12 when x = 3, what is the constant of proportionality k?

    • 9
    • 0.25
    • 4
    • 36

  9. p is inversely proportional to q. p = 20 when q = 0.5. What is p when q = 2?

    • 40
    • 1.25
    • 5
    • 10

  10. 4 identical machines fill a tank in 9 hours. How many hours would 6 of the same machines take to fill it?

    • 4 hours
    • 6 hours
    • 13.5 hours
    • 3 hours

  11. y is directly proportional to x. y = 3.6 when x = 0.8. What is y when x = 2.5?

    • 2.25
    • 9.0
    • 12.5
    • 11.25

  12. In direct proportion, which quantity stays constant as the values change?

    • The sum y + x
    • The difference y − x
    • The product y × x
    • The ratio y ÷ x

  13. Which situation shows inverse proportion?

    • Cost of apples, when the mass of apples changes
    • Area of a circle, when its radius changes
    • Number of sweets bought, when the total cost changes
    • Time taken to travel a fixed distance, when the speed changes

  14. (H) y is directly proportional to x². When x = 2, y = 20. What is y when x = 5?

    • 100
    • 125
    • 50
    • 25

  15. The time t for a job is inversely proportional to the number of workers n. 10 workers take 15 days. How many workers finish the job in 12 days?

    • 18.75 workers
    • 15 workers
    • 12.5 workers
    • 8 workers

  16. P is directly proportional to Q, and Q is inversely proportional to R. If R doubles, what happens to P?

    • P halves
    • P quarters
    • P stays the same
    • P doubles

  17. x = 2 gives y = 30 and x = 5 gives y = 12 in an inverse relationship. What is y when x = 10?

    • 24
    • 3
    • 12
    • 6

  18. A tank fills in 40 minutes with 3 equal pipes. How long would 5 of the same pipes take?

    • 66.7 minutes
    • 15 minutes
    • 24 minutes
    • 32 minutes

  19. A bag of rice is directly proportional to its price: 2 kg costs £3.40. What does 500 g cost?

    • £0.85
    • £0.34
    • £6.80
    • £1.70

  20. For y = k/x, y = 0.25 when x = 8. What is the value of k?

    • 0.03125
    • 32
    • 6.25
    • 2

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