Question

The captain of a cricket team of $11$ players is $25$ 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 in $1$ year less than the average age of the whole team. The average of the whole team is

• A. $21.5$year
• B. $22$ year
• C. $22.5$ year
• D. $23$ year

Answer 1

Answer: (B)

$22$ year

Let $a_1,a_2,a_3,....$ all be the 11 players of the team.
Let $a_{10}$ represents the captain and $a_{11}$ represents the wicketkeeper.
Given : Age of captain = 25 yrs., i.e., $a_{10}=25$
And age of wicketkeeper = 25 + 3 = 28 yrs, i.e, $a_{11}=28$
To find : $\frac{a_1+a_2+...+a_9+a_{10}+a_{11}}{11}$
According to the question,
$\frac{a_1+...+a_9}{9}=\frac{a_1+...+a_9+a_{10}+a_{11}}{11}-1$
$\Rightarrow \frac{a_1+...+a_9}{9}=\frac{(a_1+...+a_9+25+28)-11}{11}$
$\Rightarrow (a_1+...+a_9)=\frac{9(a_1+...+a_9)+9\times 53-99}{11}$
$\Rightarrow \frac{2}{11}(a_1+...+a_9)=\frac{477-99}{11}=\frac{378}{11}$
$\Rightarrow a_1+...+a_9=189$
$\therefore \frac{a_1+...+a_9+a_{10}+a_{11}}{11}=\frac{189+53}{11}=\frac{242}{11}=22$.
$\therefore$ Average age of whole team = 22 years.