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The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?

Correct answer: C. 12

  • A. 22
  • B. 24
  • C. 12
  • D. 8

Explanation

For 10 persons, a decrease of 3 years in the average means the total age decreases by 10 x 3 = 30 years. Since the replaced person's age was 42 years, the new person's age is 42 - 30 = 12 years. The likely mistake is choosing 24 years by subtracting 3 directly from 42, confusing the average decrease with the total decrease.

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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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