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The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average of the team?

Correct answer: A. 23 years

  • A. 23 years
  • B. 24 years
  • C. 25 years
  • D. None of these

Explanation

Let the team's average age be x years, so the total age is 11x years. The captain and wicketkeeper together are 26 + 29 = 55 years, and the remaining nine players have average x - 1 years, so 11x - 55 = 9(x - 1). Solving gives 2x = 46, hence x = 23 years. The likely error is choosing 24 years by subtracting one year from the whole-team average without accounting for the two excluded players.

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About Averages

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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