Question

The captain of a cricket team of 11 members is 31 years old, and the wicket keeper is 4 years older. If the ages of these two are excluded, the average age of the remaining players is two year less than the average age of the whole team What is the average age of the team?​

Answer 1

Step-by-step explanation:

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Answer 2

The correct answer is

Given: Age of Captain = 31

Relation between age of Captain and Keeper.

To Find: Average age of team.

Solution:

Age of Keeper = Age of Captain + 4

= 31 + 4

Age of Keeper = 35

Average age of team = $\frac{35 + 31+(sum of age of 10 players)}{12}$

Average age of team after excluding Captain and Keeper = $\frac{(sum of age of 10 players)}{10}$

Now, according to the condition "the ages of these two are excluded, the average age of the remaining players is two year less than the average age of the whole team".

Average age of remaining players = Average of whole team - 2

$\frac{(sum of age of 10 players)}{10}$ =  $\frac{35 + 31+(sum of age of 10 players)}{12}$ - 2

$\frac{(sum of age of 10 players)}{10}$ = $\frac{35 + 31+(sum of age of 10 players)-24}{12}$

12(sum of ages of 10 players) = 10(sum of ages of 10 players) + 420

2(sum of ages of 10 players) = 420

sum of ages of 10 players = 210

So, now put the value of this in formula of average age of whole team written above.

Average age = $\frac{210+31+35}{12}$

= 23

Hence, the average age of whole team is 23.

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