The average age of the Indian cricket team playing in the Capetown test match is 28 years. If the average age of 10 players except the Captain is 27.8 years, then the age of the Captain is:
30 Years
Solving for the Captain's Age
This problem requires calculating the age of the captain based on the average ages provided for the entire cricket team and the team excluding the captain.
Understanding Average Age Calculation
The average age is calculated by dividing the sum of all ages by the number of individuals. Therefore, the sum of ages can be found by multiplying the average age by the number of individuals.
Step-by-Step Solution
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Calculate the total age of all 11 players:
The average age of the Indian cricket team (11 players) is 28 years. Total Age (11 players) = Average Age $\times$ Number of Players
Total Age (11 players) = $28 \times 11 = 308$ years. -
Calculate the total age of the 10 players (excluding the captain):
The average age of 10 players (excluding the captain) is 27.8 years. Total Age (10 players) = Average Age $\times$ Number of Players
Total Age (10 players) = $27.8 \times 10 = 278$ years. -
Determine the captain's age:
The captain's age is the difference between the total age of all 11 players and the total age of the 10 players. Captain's Age = Total Age (11 players) - Total Age (10 players)
Captain's Age = $308 - 278 = 30$ years.
The age of the Captain is 30 years.
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