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Grade 9 · Ratio & Proportion
Direct & Indirect Proportion
MEMORANDUM
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Mark
  / 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    If 5 books cost R125, what do 8 books cost?
    (2)
    One book R25 → R200 (direct)✓✓ (2)
  2. 2
    If 3 kg of rice costs R45, what does 7 kg cost?
    (2)
    R15/kg → R105 (direct)✓✓ (2)
  3. 3
    8 workers finish a job in 6 days. How long would 4 workers take?
    (2)
    48 ÷ 4 = 12 days (indirect)✓✓ (2)
  4. 4
    5 taps fill a tank in 12 minutes. How long would 10 taps take?
    (2)
    60 ÷ 10 = 6 minutes (indirect)✓✓ (2)
  5. 5
    A journey takes 4 hours at 90 km/h. How long at 120 km/h?
    (2)
    360 ÷ 120 = 3 hours (indirect)✓✓ (2)
  6. 6
    Is 'number of workers vs time taken' direct or indirect?
    (2)
    Indirect — more workers, less time.✓✓ (2)
  7. 7
    Is 'litres of petrol vs cost' direct or indirect?
    (2)
    Direct — more litres, more cost.✓✓ (2)
  8. 8
    y is directly proportional to x, and y = 20 when x = 4. Find k.
    (2)
    k = 20 ÷ 4 = 5, so y = 5x✓✓ (2)
TOTAL: 16 marks
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