Ratios and proportion in workplace problems: Practice 2 (Intermediate)

Combine linked ratios, staff transfers, changing budgets and direct or inverse scaling in ten original 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. Label each quantity, find the value of a ratio part, and reconstruct counts before a transfer or addition. Match the shared component when joining two ratios. For a fixed workload, check whether the required relationship is inverse.

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 15 minutes and uses the scoring shown on its rules screen. Those settings are not official assessment rules.

Practise with feedback Optional timed challenge

  1. 1. Three stock counts satisfy A:B = 3:4 and B:C = 6:5. What is A:B:C in simplest whole-number form?
    1. 3:4:5
    2. 6:8:5
    3. 9:12:10
    4. 9:12:15

    Reference: q-fa43b093-97 · Report this question

    Show answer and solution

    Answer: C. 9:12:10

    Make the shared B quantity twelve parts. Multiply 3:4 by three to get 9:12, and 6:5 by two to get 12:10. Combining gives A:B:C = 9:12:10. Check both original pairwise comparisons.
  2. 2. An Australian office has 64 staff split between analysts and support in the ratio 5:3. Four analysts transfer to support, with no other staffing changes. What is the new ratio of analysts to support staff?
    1. 5:4
    2. 7:9
    3. 4:3
    4. 9:7

    Reference: q-8afc4301-206 · Report this question

    Show answer and solution

    Answer: D. 9:7

    Initially the office has forty analysts and twenty-four support staff. After the transfer, the counts are 36 and 28. Simplifying 36:28 gives 9:7. A transfer subtracts from one group and adds to the other.
  3. 3. A UK store has blue and white labels in the ratio 2:7. It adds ten blue labels and no white labels, making the new ratio 4:7. How many blue labels were present originally?
    1. 10
    2. 20
    3. 25
    4. 35

    Reference: q-dc81a576-172 · Report this question

    Show answer and solution

    Answer: A. 10

    Write the original stocks as 2k and 7k. The new ratio gives (2k + 10)/(7k) = 4/7, so 2k + 10 = 4k and k = 5. The original blue stock was 2 × 5 = ten labels.
  4. 4. An Indian business allocates 88 training places between two departments in the ratio 4:7. It then adds eight places to the first department, leaving the second unchanged. What is the new ratio of first-department places to second-department places?
    1. 4:5
    2. 5:7
    3. 6:7
    4. 5:8

    Reference: q-60b46c2a-249 · Report this question

    Show answer and solution

    Answer: B. 5:7

    Initially each part is eight places, giving 32 and 56. The first department then has forty while the second still has 56. The ratio 40:56 simplifies to 5:7; the new total is 96 places.
  5. 5. A US team records correct and incorrect checks in the ratio 23:2. There are 750 checks altogether and every check is classified once. How many are correct?
    1. 600
    2. 660
    3. 690
    4. 720

    Reference: q-b0df922c-156 · Report this question

    Show answer and solution

    Answer: C. 690

    The total represents 25 parts. Each part equals 750 ÷ 25 = thirty checks. Correct checks occupy 23 parts, giving 23 × 30 = 690; the remaining sixty are incorrect.
  6. 6. A fictional ten-litre mixture contains concentrate and water in the ratio 1:4 by volume. Four litres of water are added, with no loss and additive volumes. What is the new ratio of concentrate to water?
    1. 1:4
    2. 1:5
    3. 2:7
    4. 1:6

    Reference: q-83a12222-203 · Report this question

    Show answer and solution

    Answer: D. 1:6

    The original mixture has two litres of concentrate and eight litres of water. Adding four litres of water gives two litres to twelve litres, or 1:6. The concentrate amount remains unchanged.
  7. 7. A fictional UK project allocates £6,400 of a shared cost between teams A and B in proportion to their recorded hours, which are in the ratio 9:7. How much of the cost is assigned to A?
    1. £3,600
    2. £2,800
    3. £3,200
    4. £4,000

    Reference: q-bc0f9651-185 · Report this question

    Show answer and solution

    Answer: A. £3,600

    The hours total sixteen parts, so one cost part is £6,400 ÷ 16 = £400. Team A receives nine parts, or £3,600. Team B receives £2,800; the two allocations add back to the stated £6,400 total.
  8. 8. Two US departments have budgets in the ratio 2:3. The first budget increases by 25% while the second stays unchanged. What is the new ratio of the first budget to the second?
    1. 3:4
    2. 5:6
    3. 2:3
    4. 3:5

    Reference: q-40258dbd-175 · Report this question

    Show answer and solution

    Answer: B. 5:6

    Represent the budgets by 2k and 3k. Increasing the first by 25% makes it 2.5k. The new comparison is 2.5:3, which becomes 5:6 after multiplying both sides by two.
  9. 9. Eight equally productive workers complete a fixed task in fifteen days. Assuming constant rates and no interference, how many days would twelve such workers need?
    1. 8
    2. 9
    3. 10
    4. 12

    Reference: q-ce626d04-163 · Report this question

    Show answer and solution

    Answer: C. 10

    The fixed task requires 8 × 15 = 120 worker-days. Twelve workers need 120 ÷ 12 = ten days. More workers reduce the required time under the explicitly stated constant-rate assumptions.
  10. 10. In a fictional Indian user study, 30% of participants use only mobile access and the remaining 70% use only desktop access. What is the ratio of mobile-only participants to desktop-only participants?
    1. 3:10
    2. 7:3
    3. 7:10
    4. 3:7

    Reference: q-11bf3c59-200 · Report this question

    Show answer and solution

    Answer: D. 3:7

    The two non-overlapping groups represent thirty and seventy out of every hundred participants. Their ratio is 30:70 = 3:7. The mobile share of the whole is 3/10, which is a different comparison.

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.

Continue learning