Weighted averages and combined rates: Practice 3 (Advanced)

Recover missing weights, distinguish pooled and subgroup results, and handle rounded summaries 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. Translate the required mean into an equation linking totals and weights. For changing group mixes, calculate the pooled result in each period separately. Do not treat rounded component means as exact data, and check that your denominator matches the population requested.

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. A US supplier sells 40 items at US$24 each and an unknown number at US$36 each. The average selling price across these items is US$32. How many items were sold at US$36?
    1. 40
    2. 60
    3. 100
    4. 80

    Reference: q-6d51c062-170 · Report this question

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    Answer: D. 80

    Let the unknown count be n. Total revenue is 960 + 36n and total count is 40 + n. Setting their ratio to 32 gives 960 + 36n = 1,280 + 32n, so n = 80. Check: US$3,840 divided by 120 items is US$32.
  2. 2. Two Australian teams have mean assessment scores of 48 and 66. Their combined mean is 60. What is the ratio of the number of people in the 48-point team to the number in the 66-point team?
    1. 1:2
    2. 2:1
    3. 1:3
    4. 3:1

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    Answer: A. 1:2

    For counts a and b, 48a + 66b = 60(a + b). Rearranging gives 6b = 12a, so a:b = 1:2. The 66-point team must be larger because the combined mean is closer to 66 than to 48.
  3. 3. Forty Indian trainees have a mean score of 50. Ten trainees whose mean is 35 leave and are replaced by ten trainees whose mean is 65. What is the new mean score for the forty trainees?
    1. 55
    2. 57.5
    3. 60
    4. 65

    Reference: q-1ddde235-185 · Report this question

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    Answer: B. 57.5

    The original total is 40 × 50 = 2,000. Remove 10 × 35 = 350 and add 10 × 65 = 650 to obtain 2,300. Divide by the unchanged headcount of forty: the new mean is 57.5.
  4. 4. A UK team reports a mean processing time of 14 minutes for ten jobs and 17 minutes for another twenty jobs. Each reported mean was rounded to the nearest whole minute; the unrounded means are unavailable. What can be concluded about the exact mean across all thirty jobs?
    1. It is exactly 16 minutes
    2. It is exactly 16.5 minutes
    3. It cannot be determined exactly from these rounded means
    4. It is exactly 17 minutes

    Reference: q-5febe5e9-272 · Report this question

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    Answer: C. It cannot be determined exactly from these rounded means

    Weighting the displayed means gives an estimate of 16 minutes, but the underlying means need not equal 14 and 17. Means of 13.6 and 16.6 give a pooled mean of 15.6; means of 14.4 and 17.4 give 16.4. Both pairs round to the stated summaries.
  5. 5. A US service desk handles 90 short calls averaging two minutes and ten long calls averaging ten minutes in one period. In the next period it handles twenty short calls averaging 1.5 minutes and eighty long calls averaging nine minutes. How does the overall mean call duration change?
    1. It falls by 1 minute
    2. It falls by 0.5 minutes
    3. It stays the same
    4. It rises by 4.7 minutes

    Reference: q-6141214c-284 · Report this question

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    Answer: D. It rises by 4.7 minutes

    The first mean is (90 × 2 + 10 × 10) ÷ 100 = 2.8 minutes. The next is (20 × 1.5 + 80 × 9) ÷ 100 = 7.5 minutes, a rise of 4.7. Both subgroup means fall, but the later period contains a much larger share of long calls.
  6. 6. An Australian vehicle travels 120 km at 72 km/h and returns over the same 120 km at 48 km/h, without stopping. What is its mean speed for the complete journey?
    1. 57.6 km/h
    2. 60 km/h
    3. 62.4 km/h
    4. 64 km/h

    Reference: q-45848aa1-160 · Report this question

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    Answer: A. 57.6 km/h

    The times are 120 ÷ 72 = 5/3 hours and 120 ÷ 48 = 5/2 hours. Total time is 25/6 hours for 240 km. Mean speed is 240 ÷ (25/6) = 57.6 km/h. Equal distances do not give equal time weights.
  7. 7. A UK analyst calculates a mean of 18 from 25 observations. One observation was entered as 42 but should have been 12. What is the corrected mean?
    1. 16.2
    2. 16.8
    3. 17.2
    4. 19.2

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    Answer: B. 16.8

    The recorded total was 25 × 18 = 450. Correcting the observation subtracts 42 and adds 12, leaving 420. The number of observations remains 25, so the corrected mean is 420 ÷ 25 = 16.8.
  8. 8. A fictional mixture combines a 20% solution with a 50% solution to produce a 32% solution. Volumes add and all concentrations are measured by volume. What ratio of the 20% solution to the 50% solution is required?
    1. 2:3
    2. 1:2
    3. 3:2
    4. 3:1

    Reference: q-3fad366a-214 · Report this question

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    Answer: C. 3:2

    Let a and b be the two volumes. The solute equation is 0.20a + 0.50b = 0.32(a + b). Thus 0.18b = 0.12a, giving a:b = 3:2. Check: three parts at 20% and two at 50% average to 32%.
  9. 9. An Indian organisation invites 100 people in group A and 150 in group B to a survey. Eighty in A respond, of whom 60% are satisfied. In B, 120 respond, of whom 75% are satisfied. What percentage of all respondents are satisfied?
    1. 67.5%
    2. 55.2%
    3. 70%
    4. 69%

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    Answer: D. 69%

    Satisfied respondents total 80 × 0.60 + 120 × 0.75 = 48 + 90 = 138. There are 200 respondents, so the share is 138 ÷ 200 × 100 = 69%. The 250 invitees are not the denominator requested.
  10. 10. A fictional US assessment combines a written score of 80 and an interview score of 60 using positive percentage weights that sum to 100%. The combined score is 73. What percentage weight is assigned to the written assessment?
    1. 65%
    2. 60%
    3. 50%
    4. 73%

    Reference: q-577602ab-226 · Report this question

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    Answer: A. 65%

    Let w be the written weight as a fraction. Then 80w + 60(1 − w) = 73, giving 20w = 13 and w = 0.65. The written weight is 65%; the remaining 35% goes to the interview.

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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