Aptitude - Average - Discussion

Captain age is =26,
Wicketkeeper age is 3 years older than captain that is =26+3=29,
Average of whole team=((Y+26+29)/11)=X,
X=average of the whole team,
Y =total age of remaining 9 members.
Total age of the whole team,
=(Y+26+29)=11X ---> Eq1.

2part
Two are excluded.
So remaining people are 9.
Average of remaining is 1 year less than the whole team,
That is =X-1,
Average of 9 members =(X-1)*Y/9,
Total age of 9 members =Y=9*(X-1) ---> Eq2.

Substitute eq2 in eq 1.
26+29+9X-9 = 11X,
46 = 2X,
X = 23.

1. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older

Step1. Let Avg age of whole team be x except the captain and wicketkeeper.

we can write as eq: (X+26+29)/11

Step2.If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team

Means x/9=((X+26+29)/11)-1
(x/9)+1=(x+55)/11
11x+99=9x+495
2x=396
x=198
Avg. age of whole team be x+55/11=253/11=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.

Let Avg age of dull team be x.

So acc to formula sum/n=avg----> equation 1)
We have 26+29+ 9 members of cricket team / 11 = x ---> equation 2)

Now Acc to ques: the average age of the remaining players is one year less than the average age of the whole team if those two players are excluded so again putting in eq 1,

9 members / 9 = x- 1 ----> equation 3.

where x is avg of the whole team

Get the value of 9 members from equation 2 and place it in eq 3.
We will get the answer as 23.

@Angana,

Let x=age.

11x is the age of all 11 members. but since the captain and wicket keepers age is given, equation will be:
11x-(26+(26+3))
=11x-55.

Now out off 11 members, we are given the ages of 2 members. so v have to find the age of 9 members.the age of 9 members, according to the question is one year less than the average age of the whole team. that is x-1. so equation will be:
9(x-1)
=9x-9.

Putting both equations together,

11x-55 = 9x-9
11x-9x = 55-9
2x = 46.
x = 23.

Let Avg age of dull team be x
so acc to formula sum/n=avg----equation 1)

we have 26+29+ 9 members of cricket team / 11 = x --- equation 2)

Now Acc to ques: the average age of the remaining players is one year less than the average age of the whole team if those two players are excluded so again putting in eq 1

9 members / 9 = x- 1 ---- equation 3

where x is avg of whole team

get the value of 9 members from equation 2 and place it in eq 3
we will get the ans as 23

Assume average of 11 people = x.

Total age/11 = x.

So total age = 11 x.

Then, One person age given i.e. 26 year.

Keeper is 3 year older so, 26+3 = 29 year.

By excluding the age of both person average become less than one year. i.e x-1.

Then total people is, 11-2 = 9.

Total age of both person = 26+29 = 55 years.

Total age of 9 people = 11x-55.

11x-55/9 = x-1.

11x-55 = 9x-9.

2x = 46.

x = 23.

So the average age of team is 23 year.

Let the sum of the ages of nine Players = x.

Then, average age of whole team = x+26+29/11.

Also, average age of nine players = x/9.

But average age of nine players = (average age of whole team)-1.

Therefore, x/9 = (x+26+29/11)-1.

x/9+1 = x+55/11.

On solving we get, x = 198.

Then, average age of whole team = x+55/11, substituting value of x.

Average age of whole team = 198+55/11.

Average age of whole team = 253/11 = 23 years.

Its simple problem to understanding this logic.

Lets consider Avg age of team X say.

Total members= 11*x=11X and their average is 26 years.

But wicketkeeper 3 years older so simple you can write=11X- (26+29).

The avg age remaining players 1 year less so logic is = total number players -remaining number players.

We can write = 9(x-1).

Avg age of whole team= 11x - (26+29) - 9(x-1).

Then solve to simple we get 23yrs.

We can go by option easily.

First option is 23 this is average so total age will be 23*11 i.e. 253 ok.

Now captain age is 26 and wicketkeeper age is 26 total of both is 55 if we deduct 55 from 253 we get (253-55) = 198 this is the age of remaining nine player.

Now divide with 9 because we want average 198/9 i.ee., 22 so you can see average new average is 22 (1 less than 23) so 23 is our answer.