Question

The age of the captain of a cricket team of $11$ players is $25$ years and the wicket keeper is $3$ years older than the captain if the ages of these two are excluded, the average age of the remaining players of the team becomes $1$ years less than the average age of the whole team. What is the average age of the whole team ?

• A. $18$ years
• B. $22$ years
• C. $25$ years
• D. $23$ years

Answer 1

The correct option is B $22$ years

Let the average age of the total team be $x$

The team has $11$ members.

Given that, age of the team captain is $25$ years.

The wicket keeper age is $3$ years older than captain

Therefore, wicket keeper age is $25+3=28$ years.

Given that average age of the team excluding captain and wicket keeper is $1$ less than the average age of the team.

Therefore, the average age of the team excluding captain and wicket keeper is $x-1$

$⟹x-1=\frac{\text{sum of 9 member's ages}}{9}$

sum of $9$ member's ages $=9(x-1)$ --------(1)

The average age of the whole team is $\frac{\text{sum of 9 member's ages+25+28}}{11}$

$⟹x=\frac{\text{sum of 9 member's ages+53}}{11}$

$⟹x=\frac{9(x-1)+53}{11}$ (from (1))

$⟹2x=44⟹x=22$

Therefore the average of the whole team is $22$ years.