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The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is___________?

Correct answer: C. 40 years

  • A. 35 years
  • B. 30 years
  • C. 40 years
  • D. None of these

Explanation

Three years ago, the combined age of the three people was 3 x 27 = 81 years, so their present combined age is 81 + 3 x 3 = 90 years. Five years ago, the wife's and child's combined age was 2 x 20 = 40 years, so their present combined age is 40 + 2 x 5 = 50 years. Therefore, the husband's present age is 90 - 50 = 40 years. The likely mistake is choosing 30 years by not adjusting both past averages to present ages.

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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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