Aptitude - Average - Discussion

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.

Let 9 Players Avg = P9
Let 11 Players Avg = x

So,
(P9 + 26 + 29) / 11 = x ------------> (Eq 1)

P9 / 9 = x -1 (Total Average is less than 1 if we exclude 26 (Cap.) and 29 (Wk))

or x = 1 + (P9 / 9) ===== or ==== x = ( P9 + 9 ) / 9 -------------> (Eq 2)

Put x value from Eq 2 to Eq 1

(P9 + 26 + 29) / 11 = ( P9 + 9 ) / 9

9 P9 + 234 + 261 = 11 P9 + 99 --------> Cross Multiplication
11 P9 - 9 P9 = 234 + 261 -99 = 495 - 99 = 396
2 P9 = 396
P9 = 198

Average of 9 Players is 198

Average of 11 Players is = (198 + 26 + 29) / 11
= 253 / 11
= 23

Team Average is 23.

Hope it is helpful to understand.

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..

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.

For the answer to question how 9 (x-1) came?

Let x be the Avg of the whole team 5.
(sum of the ages of all players) / (no. Of players) = Avg.

=>sum/11 = x.
=>sum =11x ------> (1 equation).

Similarly, Avg of 9 players is less than Avg of a team.
(sum of ages of 9 players) / (no. Of players) = x - 1.

=> (sum of ages of 9 players) /9 = x - 1.
=> (sum of ages of 9 players) =9 (x - 1) ---------> 2nd equation.

(sum of ages of 9 players) = (sum of ages of 11 players) - (captain and keepers age).

Now from eqn 1.
=> (sum of ages of 9 players) =11x - (26 + 29).

Put this in eqn 2.
11x - (26 + 29) = 9 (x - 1).

This answer can't be made more simple,

According to formula: Sum of people/Total number of people = Average

Assume:

Sum of people = W.

Total number of people = 11------given.

Average = X.
W/11 = X.

W = 11X --Since we need average not weight.

NOW it is said that exclude the weight of captain (26) and keeper (Since 3 year elder his age become 29). So that average become less than one year.

W-(26+29)/9 = X-1------(2)

Since two people have been excluded number of people remain 9.

Put equation 1 in equation 2.

= 11X-55 = 9(X-1).

2X = 55-9.
2X = 46.
X = 23.

So the average age after two people excluded is 23.

Hope you understand guys. Thank you.

A captain age is 26 years old.

Then wicket keeper is 3 years older than as captain. So (26+3)=29.
Total= avg* no of observation,
x= 11 players average, y= total of 9 players.
At 11players,
y+26+29= x* 11.
y+55= 11x -----------> (1)
At 2 players excluded, so 9 players,
As formula. y= (x-1)* 9 -----------> (2)
(2) substituting by (1):

(x-1)* 9+55= 11x,
9x-9+55= 11x,
2x= 46,
X= 23.

So average of whole team so 23 years old.

Given,
Captain age= 26.
Wicketkeeper age = 29.

Step 1.
We know that,
Average = sum of all number/total number.

Consider, sum of all number =x.
So, Average =y.

From the formula, the average for the whole team.
X /11 = y
X= 11y --> Equation 1.

Step 2
Average for 9 players.
X - 55 / 9 = y-1. From condition given in problem
55 is the sum of captain and wk.
X is a sum of the whole player.
Y is an average of the whole player.

Step 3.
Put equation 1 in step 2.
We get,
(11 y -55)/ 9 = (y-1).
11y-55=9y-9,
2y=46,
y =23.
Y is average of whole member.

Explanation:
Let x be the total ages of everyone in the team except the captain and wicketkeeper:
x / 9 = Avg. age of everyone except capt. and wkt keeper
(x + 26 + 29) / 11 = (x + 55) / 11 = Avg. age of full team
So:
(x + 55)/11 = (x/9) + 1 (since the average for team without those two is one less than the average with those two)
Add that 1 and you get (x+9)/9 and then cross multiply to get:
11x + 99 = 9x + 495
x = 198
So average age of team:
198 + 55 = 253
253/11 = 23 years

Much longer than explanation given above but it explains things better.

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.