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

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

Solution:
Let the average age of the whole team by x years.
Total age of the whole team 11x years
Age of the captain 26 years
Age of the wiket-keeper 26 + 3 = 29 years

The average age of the remaining players after excluding the ages of captain and wicketkeeper = x - 1
∴ Total age of the players without the ages of captain and wicketkeeper = 9(x - 1)

We can say,
11x - (26 + 29) = 9(x - 1)
⇒ 11x - 55 = 9x - 9
⇒ 11x - 9x = - 9 + 55
⇒ 2x = 46
∴ x = 23 Years.

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