Ratios and proportion in workplace problems: Practice 3 (Advanced)

Use ratio equations, multiple resource factors and combined batches to solve ten original workplace problems.

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.

A calculator is allowed. Represent unknown quantities as ratio parts multiplied by a common factor. Apply changes to the actual quantities before forming the new ratio. For mixtures, recover component amounts in each batch before combining.

Answer keys and reasoning checked 19 October 2026. These checks do not establish psychometric validity.

Feedback mode has no time limit or negative marking. The optional timed challenge allows 20 minutes and uses the scoring shown on its rules screen. Those settings are not official assessment rules.

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  1. 1. Two Australian teams have headcounts in the ratio 7:5. Twelve people join only the second team, changing the ratio to 7:8. What was the combined headcount before they joined?
    1. 48
    2. 60
    3. 72
    4. 84

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    Answer: A. 48

    Write the original headcounts as 7k and 5k. Since (7k)/(5k + 12) = 7/8, cross-multiplication gives 56k = 35k + 84, so k = 4. The original total was 12k = 48.
  2. 2. A UK warehouse has two stocks in the ratio 3:7. Eighteen units are added to each stock, changing their ratio to 3:5. What was the original size of the smaller stock?
    1. 12
    2. 18
    3. 24
    4. 36

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    Answer: B. 18

    Let the original stocks be 3k and 7k. Then 5(3k + 18) = 3(7k + 18), giving 15k + 90 = 21k + 54. Thus k = 6 and the smaller original stock was eighteen. Equal additions do not preserve a ratio.
  3. 3. Six identical machines produce 4,800 units in eight operating hours. Assuming constant rates and no other production limit, how many operating hours would nine such machines need to produce 9,000 units?
    1. 6
    2. 8
    3. 10
    4. 12

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    Answer: C. 10

    Each machine produces 4,800 ÷ (6 × 8) = 100 units per operating hour. Nine machines produce 900 units per hour, so 9,000 units require ten hours. Both machine count and operating time affect output.
  4. 4. Three Indian project allocations satisfy A:B = 4:9 and B:C = 6:5. Their total is INR 2,050. How much is allocated to A?
    1. INR 300
    2. INR 350
    3. INR 450
    4. INR 400

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    Answer: D. INR 400

    Match the B parts at eighteen: A:B = 8:18 and B:C = 18:15. The combined ratio 8:18:15 has 41 parts. Each part is INR 50, so A receives INR 400.
  5. 5. Two US processors have constant processing rates in the ratio A:B = 3:5. Each works alone on an identical fixed workload. What is the ratio of the completion times A:B?
    1. 5:3
    2. 3:5
    3. 3:8
    4. 5:8

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    Answer: A. 5:3

    For the same workload, completion time is inversely proportional to processing rate. The times are proportional to 1/3 and 1/5, giving 5:3. The slower processor A must take longer.
  6. 6. A fictional UK review has approved and declined submissions in the ratio 11:4. Thirty additional submissions are approved, with no other changes, making the ratio 7:2. How many submissions had been declined?
    1. 20
    2. 40
    3. 60
    4. 80

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    Answer: B. 40

    Write the original counts as 11k and 4k. Then 2(11k + 30) = 7(4k), giving 22k + 60 = 28k and k = 10. The declined count stays at 4k = forty.
  7. 7. A fictional thirty-litre batch contains liquids A and B in the ratio 2:3. A separate twenty-litre batch contains A and B in the ratio 3:1. Assuming no loss and additive volumes, what is the ratio of A to B after combining the batches?
    1. 5:4
    2. 3:2
    3. 27:23
    4. 23:27

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    Answer: C. 27:23

    The first batch contains twelve litres of A and eighteen of B. The second contains fifteen of A and five of B. Combined amounts are 27 and 23 litres, giving 27:23. Adding ratio parts without considering batch sizes would be wrong.
  8. 8. Two Australian departments have budgets in the ratio 2:5. The first spends 50% of its budget and the second spends 80% of its budget. What is the ratio of their unspent amounts, first to second?
    1. 2:5
    2. 1:2
    3. 5:2
    4. 1:1

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    Answer: D. 1:1

    Represent the budgets as 2k and 5k. The first retains 50% of 2k, or k; the second retains 20% of 5k, also k. Their unspent amounts are therefore in the ratio 1:1.
  9. 9. A fictional recipe combines ingredients A, B and C by mass in the ratio 2:3:5. Preparation loses exactly 10% of each ingredient’s mass. The finished batch contains 27 kg of B. What was the total mass of all ingredients before preparation?
    1. 100 kg
    2. 90 kg
    3. 110 kg
    4. 120 kg

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    Answer: A. 100 kg

    Before the 10% loss, B weighed 27 ÷ 0.90 = thirty kilograms. B represents three of the ten original ratio parts, so one part is ten kilograms. The original total was 100 kg. Equal proportional losses preserve the component ratio.
  10. 10. Two Indian teams have output quantities in the ratio 4:5. The first quantity increases by 20% and the second decreases by 20%. What is the new ratio of the first output to the second?
    1. 1:1
    2. 6:5
    3. 4:5
    4. 5:6

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    Answer: B. 6:5

    Use starting quantities 4k and 5k. The new quantities are 4.8k and 4k, so the new ratio is 4.8:4 = 6:5. Opposite percentage changes apply to different original quantities.

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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