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 age of the team?23 years24 years25 yearsNone of these
Question
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 age of the team?23 years24 years25 yearsNone of these
Solution
Let's solve this step by step:
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The total number of players in the team is 11. The captain and the wicket keeper are 2 people. So, the number of remaining players is 11 - 2 = 9.
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The age of the captain is 26 years old and the wicket keeper is 3 years older, so the wicket keeper is 26 + 3 = 29 years old.
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The combined age of the captain and the wicket keeper is 26 + 29 = 55 years.
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Let's denote the average age of the whole team as x. So, the total age of the team is 11x.
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The average age of the remaining players is one year less than the average age of the whole team, so it's x - 1. The total age of the remaining players is therefore 9(x - 1).
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The total age of the team is the sum of the ages of the captain, the wicket keeper, and the remaining players. So, we have the equation: 55 + 9(x - 1) = 11x.
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Solving this equation for x gives us x = 24.
So, the average age of the team is 24 years.
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