Aptitude - Average - Discussion

26 + 29 = 55,
55 - 9 = 46,
46/2 = 23.

The cricket team of 11 members.

Leader = 26 years old.
Wicket keeper= 26 + 3 = 29 years old.
these two member are excluded so = 11-2 =9.
the 9 members' average is 1 year less than the whole team's average.
x-whole team average age.
9 member(average age -1).
9(x-1) = sum of 9 members age.

Formula: average=sum of all members age/no. of member in team.
x = (26+29+(9[x-1]))/11.
11x = 55+9(x-1),
11x = 55+9x-9,
11x = 46+9x,
11x-9x = 46,
2x = 46,
x = 23.
The average age of the whole team is 23.

By taking 23 from the given options we can solve it easily.

Let's do it,
23 x 11 = 253.
253 - 55 = 198.
198/9 = 22.
22<23 by 1.


The sum of 11 members is 11 * 23 = 253.
253-55(captain 26yr + 29 wicket-keeper) = 198.
198/9 (9 is the remaining members excluding captain and wicketkeeper) = 22.
So, 22yr average of (9 members) is less than 23 (11 whole team) by an average 1 year.

Thanks for explaining the answer @Iman.

11x-(26+29) = 9(x-1).
11x-55 = 9x-9.
2x = 64.
x = 32.

By Balancing two sides.

x = average.
9x + 26 + 29/11 = (x/9)+1.
9x + 55/11 = x + 9/9,
9x + 5 = x,
9 x 5 = 2x,
45 = 2x,
45/2 = x.
x = 22.5 (round off)
x = 23.

From the question,

= Sum of 9 players + (26+29)/11 = x-------> Eqn. 1
= Sum of 9 players/9 = x-1---------> Eqn. 2

9x-9+26+29 = 11x,
46 = 2x,
x = 23.

Let's apply simple formula.

Weight of persons left= previous average weight-no.of persons excluding the person left decrease in weight.

As we know two people left. One is equal to a weight of 26 and the other is 29. so weight of persons left = 29+26 = 55.

Consider weight as X hence previous average weight of 11 Players will be 11X.

after excluding, 2 members number of players will be 11-2=9.
As in the statement, it is mentioned the average age of the remaining players is one year less than the average age of the whole team. it means (x-1)

Simple, put these values in the above-mentioned formula

55 = 11X-9(x-1),
55 = 11x-9x+9,
55- 9 = 2x,
46 = 2x,
23 = X.
That's it.
Hope you find it easy..

Thank you for giving a clear explanation @Panddu.

Very good explanation, Thanks @Panddu.