[23 years] The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older.

For Competitive Exams

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. Find out the average age of the team.

23 years

20 years

24 years

21 years

Explanation:

Number of members in the team = 11

Let the average age of of the team = $x$

=> $\dfrac{\text{Sum of ages of all 11 members}}{11} = x$

=> Sum of the ages of all 11 members = $11x$

Age of the captain = 26

Age of the wicket keeper = 26 + 3 = 29

Sum of the ages of 9 members of the team excluding captain and wicket keeper

$= 11$x$ - 26 - 29 = 11$x$ - 55$

Average age of 9 members of the team excluding captain and wicket keeper

$=\dfrac{11x - 55 }{9}$

Given that $\dfrac{11x - 55 }{9} = \left(x - 1\right)$

$\Rightarrow 11x - 55 = 9 \left(x - 1\right)$

$\Rightarrow 11x - 55 = 9x - 9$

$\Rightarrow 2x = 46$

$\Rightarrow x = \dfrac{46}{2} = 23\text{ years}$

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