Weighted averages and combined rates: Practice 2 (Intermediate)

Choose the right weights for staffing, prices, service rates and course scores in ten original problems.

Instructions for this set

Use the actual group size, time or unit count as the weight. A calculator is allowed. Do not assume equal weights unless stated.

A calculator is allowed. Label the quantity each average describes. Multiply each average by its matching count to recover a total, then divide the combined total by the combined count. For a missing group, subtract known totals before dividing. Keep the original units throughout.

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.

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  1. 1. A US operations team has 12 staff completing an average of 18 checks each per day. A second team has 20 staff averaging 30 checks each. What is the combined daily average per staff member?
    1. 24
    2. 25.5
    3. 26
    4. 27

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    Answer: B. 25.5

    The teams complete 12 × 18 + 20 × 30 = 816 checks altogether. Divide by 32 staff to obtain 25.5 checks per staff member. Averaging 18 and 30 directly would give each team equal weight despite their different sizes.
  2. 2. A UK retailer sells 25 notebooks at £8 each and 75 at £12 each. What is the average selling price per notebook across these sales?
    1. £10
    2. £10.50
    3. £11
    4. £11.50

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    Answer: C. £11

    Total revenue is 25 × 8 + 75 × 12 = £1,100 from 100 notebooks. Divide revenue by the number sold: £11 per notebook. The larger £12 group carries three times as much weight as the £8 group.
  3. 3. Fifty Australian staff complete an average of 42 training tasks each. Twenty of them average 36 tasks each. What is the average for the other thirty staff?
    1. 40
    2. 44
    3. 45
    4. 46

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    Answer: D. 46

    All staff complete 50 × 42 = 2,100 tasks. The known group completes 20 × 36 = 720. The remaining 1,380 tasks belong to thirty staff, giving an average of 46. Subtract totals, not the two averages.
  4. 4. An Indian warehouse has 24 parcels with an average mass of 7.5 kg. Four parcels averaging 10.5 kg are removed. What is the average mass of the twenty remaining parcels?
    1. 6.9 kg
    2. 7.0 kg
    3. 7.5 kg
    4. 8.1 kg

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    Answer: A. 6.9 kg

    The original total mass is 24 × 7.5 = 180 kg. The removed parcels weigh 4 × 10.5 = 42 kg, leaving 138 kg. Divide by the twenty remaining parcels to obtain 6.9 kg. The removed parcels were heavier than the original mean, so the mean falls.
  5. 5. A UK training cohort of eighteen people has an average score of 64. Six more people with an average score of 80 join. What is the combined average score?
    1. 66
    2. 68
    3. 70
    4. 72

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    Answer: B. 68

    The combined score total is 18 × 64 + 6 × 80 = 1,632. There are 24 people, so the mean is 1,632 ÷ 24 = 68. The original group is three times larger and therefore has three times the weight.
  6. 6. A fictional course gives 25% weight to a project score of 72, 35% to a presentation score of 80 and 40% to a final assessment. All components are scored out of 100. What final assessment score is needed for an overall score of 82?
    1. 82
    2. 85
    3. 90
    4. 95

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    Answer: C. 90

    The first two components contribute 0.25 × 72 + 0.35 × 80 = 46 points. The final assessment must contribute 82 − 46 = 36. Its score must therefore be 36 ÷ 0.40 = 90 out of 100.
  7. 7. A US branch handles 120 requests and completes 75% on time. Another handles 80 requests and completes 90% on time. What percentage of all 200 requests are completed on time?
    1. 80%
    2. 82.5%
    3. 85%
    4. 81%

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    Answer: D. 81%

    The on-time counts are 120 × 0.75 = 90 and 80 × 0.90 = 72. Together that is 162 out of 200 requests, or 81%. The simple mean of 75% and 90% would ignore the different request counts.
  8. 8. An Australian call centre handles 90 calls averaging four minutes each and 30 calls averaging eight minutes each. What is the average duration across all 120 calls?
    1. 5 minutes
    2. 6 minutes
    3. 6.5 minutes
    4. 7 minutes

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    Answer: A. 5 minutes

    Total call time is 90 × 4 + 30 × 8 = 600 minutes. Dividing by 120 calls gives five minutes per call. Call counts supply the weights; weighting by the two group durations would answer a different question.
  9. 9. A UK driver travels for 45 minutes at 40 miles per hour and then for 15 minutes at 64 miles per hour, without stopping. What is the average speed for the full hour?
    1. 44 mph
    2. 46 mph
    3. 48 mph
    4. 52 mph

    Reference: q-490a5fd7-165 · Report this question

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    Answer: B. 46 mph

    The first stage covers 0.75 × 40 = 30 miles; the second covers 0.25 × 64 = 16 miles. The total is 46 miles in one hour, so the mean speed is 46 mph. The speeds must be weighted by time, not treated equally.
  10. 10. A fictional batch mixes 12 litres of a 15% solution with 18 litres of a 35% solution. Assuming volumes add and concentrations are measured by volume, what is the final concentration?
    1. 25%
    2. 26%
    3. 27%
    4. 30%

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    Answer: C. 27%

    The solute volumes are 12 × 0.15 = 1.8 litres and 18 × 0.35 = 6.3 litres. Their sum is 8.1 litres in a 30-litre mixture. The concentration is 8.1 ÷ 30 × 100 = 27%.

Review your method

Return to the weighted averages and combined rates 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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