Question

The captain of a cricket team of 11 members is 26 years old and the wicketkeeper is 3 years older than the captain. If the ages of these two are excluded, the average age of the remaining players is one year less than the whole team. What is the average age of the team?

• A. $23$ years
• B. $24$ years
• C. $25$ years
• D. None of these

Answer 1

The correct option is A $23$ years

Given that the captain age is $26$ years.

Given that wicket-keeper age is $3$ years older than the captain.

Therefore, the wicket-keeper age is $26+3=29$ years.

Let the average age of the whole team be $\overline{x}$

Therefore, $\overline{x}=\frac{\text{sum of the ages of the whole team members}}{11}$

$⟹11\overline{x}=26+29+\text{sum of the ages of the remaining 9 team members}$

$⟹\text{sum of the ages of the remaining 9 team members}=11\overline{x}-55$ -------(1)

Given that the average of the remaining 9 players is one year less the whole team.

Therefore, average of the remaining team is $\overline{x}-1$

$⟹\overline{x}-1=\frac{\text{sum of the ages of the remaining 9 team members}}{9}$

$⟹\text{sum of the ages of the remaining 9 team members}=9\overline{x}-9$ ------(2)

from (1) and (2) we get

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

$⟹11\overline{x}-9\overline{x}=55-9$

$⟹2\overline{x}=46$

$⟹\overline{x}=23$

Therefore, the average of the team is $23$ years