Aptitude - Average - Discussion

Thank you for giving a clear explanation @Panddu.

Let the average age of whole team = x.
Sum of ages of captain and wicket keeper is 26+29 = 55.

We know the average formula:-

Average = Sum of quantities / No.of quantities.
Now according to given condition.
x = Sum of ages of 11 players/ 11.
So we got 11x = Sum of ages of 11 players.

But we have to find the average age of 9 players excluding the age of captain and the keeper which is 1 year less than the whole team which means we will write (x-1) so now according to average formula we will write.

Avg age of 9 players = 11x - 55/9.

which means,
x-1 = 11x - 55/9.
9x - 9 = 11x - 55.
55 - 9 = 11x - 9x.
46 = 2x.
So x = 23.

Which means the avg age of whole team is 23.

(X/11) = Y.
X = 11Y,
26 + 29 = 55,
(X-55)/9 = (Y-1)9,
Y = 23.

To be simple;
Avg - 55 = avg-1( bcoz if excluded 1 yr less than avg),
Avg = 23.

Thanks for explaining the answer @Iman.

Easy method:

In the whole team, 11 members are there.
Captain age is 26 and wicket-keeper age is 3 yr older than captain means 29.
So 26+29 = 55.

Then 2 player excluded and 1 year less than,
Now only 9 players left 9 multiply by 1 = 9.
55-9 = 46 divide by 2 = 23 answer.

(X-1)? came? Please anyone explain me.

Let x be average of 11 people or team.

Total age of two-person is 26 + 29 = 55.
Total age of 11 people be= 11 * x = 11x.
It says when 2 people excluded avg is decreased by 1 so, it is = x - 1.
Now find the avg of 9 members.

{11x(total age) - 55( two person)}/9 = X-1.
So, 11x-55 = 9(x-1) "take 9 to other side".
Then solve it.

Very good explanation, Thanks @Panddu.

Let us Assume that the Average age of 11 members be x.

Then the Total Age of 11 members is 11 * x.

But Given That the age of Captain and Wicket Keeper is (26+29) = 55.

From Above the total Age of Remaining 9 members in the Team will be (11 * x - 55).

Let us Assume that the above step as number (1).

Given Another Condition is the Average of remaining team members is one less than that of all the average of team members i.e., (x-1).

Then from that the total Age of remaining 9 members be [9*(x-1)].

Let us Assume that the above step as number (2).

So From the Above Explanation step 1 and 2 are same .

By Equating step (1) and step (2) It will be,

==> (11x - 55) = [9(x - 1)]
==> (11x - 55) = 9x - 9
==> 11x - 9x = 55 - 9
==> 2x = 46
==> x = 23.

Therefore the Average Age of the all team members will be 23 Years.