Ratios and proportion in workplace problems: Practice 1 (Foundation)

10 original teaching questions with answers and explanations.

Instructions for this set

Keep the order of the named quantities. Convert matching quantities to the same units before simplifying. Use constant-rate assumptions only where stated. A calculator is allowed. All business figures are hypothetical.

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  1. 1. A US office has fourteen support staff and twenty-one analysts. What is the simplest ratio of support staff to analysts?
    1. 2:3
    2. 3:2
    3. 2:5
    4. 7:3

    Reference: q-f628a067-121 · Report this question

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    Answer: A. 2:3

    Write the quantities in the requested order: 14:21. Divide both by seven to obtain 2:3. The support share of all staff would be 14/35; that is a different comparison.
  2. 2. A UK project budget of £4,200 is shared between design and delivery in the ratio 2:5. How much is allocated to delivery?
    1. £1,200
    2. £3,000
    3. £2,100
    4. £3,500

    Reference: q-785851ec-121 · Report this question

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    Answer: B. £3,000

    There are 2 + 5 = 7 parts altogether. Each is worth £4,200 ÷ 7 = £600. Delivery receives five parts, or £3,000; design receives the remaining £1,200.
  3. 3. An Australian store has blue and green folders in the ratio 3:8. It has 64 green folders. How many blue folders does it have?
    1. 16
    2. 21
    3. 24
    4. 32

    Reference: q-e604b8da-126 · Report this question

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    Answer: C. 24

    Eight green parts equal 64 folders, so each part is eight folders. The blue stock has three parts: 3 × 8 = 24. Use the known green quantity to determine one part.
  4. 4. An Indian team has permanent and temporary staff in the ratio 9:16. What percentage of the whole team is permanent?
    1. 9%
    2. 25%
    3. 56.25%
    4. 36%

    Reference: q-1c2324c0-116 · Report this question

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    Answer: D. 36%

    There are 25 parts in total, of which nine are permanent. The share is 9 ÷ 25 × 100 = 36%. Dividing nine by sixteen would compare permanent staff with temporary staff, not the whole team.
  5. 5. A UK workshop compares a 45-minute inspection with a 1.5-hour inspection. What is the simplest ratio of the shorter time to the longer time?
    1. 1:2
    2. 2:1
    3. 3:10
    4. 30:1

    Reference: q-929581a0-141 · Report this question

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    Answer: A. 1:2

    Convert 1.5 hours to ninety minutes. The requested ratio is 45:90, which simplifies to 1:2. Comparing the unconverted numbers 45 and 1.5 would mix incompatible units.
  6. 6. A US scanner processes 24 forms in six minutes at a constant rate. How many minutes will it take to process 36 forms at the same rate?
    1. 8
    2. 9
    3. 12
    4. 15

    Reference: q-5524c5d7-135 · Report this question

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    Answer: B. 9

    The scanner handles 24 ÷ 6 = four forms per minute. Processing 36 forms takes 36 ÷ 4 = nine minutes. At a constant rate, the required time is directly proportional to the number of forms.
  7. 7. Five identical printers working together complete a fixed job in twelve minutes. Assuming equal constant rates and no interference, how long would three of the printers take?
    1. 7.2 minutes
    2. 15 minutes
    3. 20 minutes
    4. 36 minutes

    Reference: q-ced6b82c-175 · Report this question

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    Answer: C. 20 minutes

    The fixed job requires 5 × 12 = sixty printer-minutes. Divide by three printers to obtain twenty minutes. Fewer equally productive printers need more time, so this is inverse proportion.
  8. 8. An Australian site plan uses a scale of 1:25,000. Two points are four centimetres apart on the plan. What actual distance does that represent?
    1. 0.1 km
    2. 0.25 km
    3. 10 km
    4. 1 km

    Reference: q-d16a4bb1-143 · Report this question

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    Answer: D. 1 km

    Multiply the plan distance by 25,000 to get 100,000 centimetres. One kilometre contains 100,000 centimetres, so the actual distance is one kilometre. The scale uses the same length unit on both sides.
  9. 9. A fictional recipe uses 600 grams of flour for eight equal servings. Keeping the recipe proportions unchanged, how much flour is needed for fourteen servings?
    1. 1,050 g
    2. 900 g
    3. 1,000 g
    4. 1,200 g

    Reference: q-493f3274-159 · Report this question

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    Answer: A. 1,050 g

    Each serving requires 600 ÷ 8 = 75 grams of flour. Fourteen servings therefore need 14 × 75 = 1,050 grams. Scale every ingredient by the same fourteen-eighths factor to preserve the recipe.
  10. 10. Two positive quantities are in the ratio 5:9, and the larger exceeds the smaller by 28. What is their sum?
    1. 70
    2. 98
    3. 126
    4. 196

    Reference: q-db2e5178-107 · Report this question

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    Answer: B. 98

    The difference of four parts equals 28, so one part equals seven. The quantities are 35 and 63, and their sum is 98. The given 28 represents the difference, not the total.

Review your method

Return to the ratios and proportion in workplace problems lesson and identify the reasoning step behind each mistake before repeating the set.

Choose your practice difficulty

Difficulty labels describe the steps needed in these teaching sets; they are not validated ability bands. Start with foundation practice and move on after you can explain your method.

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