Aptitude - Average - Discussion

Let the average age of the whole team by x years.

11x - (26 + 29) = 9(x -1).
11x-55=9x-9.
11x - 9x = -9+55.
2x = 46.
x = 23..
So, the average age of the team is 23 years.

How (x-1) came here?

Let average age of whole team =x.

Excluding age of 2 members,average age of remaining 9 players is:

(FORMULA--->Average=sum of data/number of items in data)
So, average age of 9 players is one year less than average age of whole team(x).

i.e (x-1)=sum/9
9(x-1)=sum.

We need to find the average age of 11 players.
We know the sum of ages of 9 players(9(x-1)), now add ages of remaining two players i.e 26+29.
Now total average of cricket team will become;
x=(9(x-1)+26+29)/11.
After simplifying this equation we will get x=23.

Age of captain = 26.
Age of wicket keeper is = 26+3 = 29.
Total age = 26+29 = 55.

Remaining team = 9.
Remove = total age - remaining team.
= 55-9 = 44.

Leave = captain+wicket keeper = 2.
44/2 = 22.

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.

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.

How 29 came because 26 years old is captain and 3 years old is wicket-keeper.

How did you get 29?

Very helpful, Thanks @Aarzoo.

26 is age of captain.

And we are given that wicket keeper is 3 year older than captain so age of wicket keeper is 29 (26+3).