The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is___________?
Correct answer: D. 31 kg
- A. 17 kg
- B. 20 kg
- C. 26 kg
- D. 31 kg
Explanation
The combined weight of A, B and C is 3 x 45 kg = 135 kg, while A + B = 2 x 40 kg = 80 kg and B + C = 2 x 43 kg = 86 kg. Adding the last two equations gives A + C + 2B = 166 kg; subtracting A + B + C = 135 kg gives B = 31 kg. The likely mistake is option c, which can result from subtracting the pair totals without accounting for B appearing twice.
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An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.
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