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?
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?
Solution
Sure, let's solve this step by step:
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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 (since there are 11 members in the team).
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The age of the captain is 26 and the wicket keeper is 3 years older, so he is 29. The total age of the captain and the wicket keeper is 26 + 29 = 55.
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If we exclude the ages of these two, we have 9 remaining players. According to the problem, the average age of these 9 players is one year less than the average age of the whole team, so it's x - 1. Therefore, the total age of these 9 players is 9 * (x - 1).
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Now, we know that the total age of the team is the sum of the total age of the captain and the wicket keeper and the total age of the remaining players. So, we can write the equation: 11x = 55 + 9 * (x - 1).
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Let's solve this equation for x. First, distribute the 9: 11x = 55 + 9x - 9.
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Then, combine like terms: 11x - 9x = 55 + 9, which simplifies to 2x = 64.
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Finally, divide by 2 to solve for x: x = 64 / 2 = 32.
So, the average age of the team is 32 years.
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