Aptitude - Average - Discussion

6. 

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. 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. What is the average age of the team?

[A]. 23 years
[B]. 24 years
[C]. 25 years
[D]. None of these

Answer: Option A

Explanation:

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

11x - (26 + 29) = 9(x -1)

11x - 9x = 46

2x = 46

x = 23.

So, average age of the team is 23 years.


Krunal said: (Jun 30, 2010)  
Can you explain how that 46 comes?

Kavita said: (Jul 21, 2010)  
11x - (26 + 29) = 9x - 9
11x - 9x = -9 + (26 + 29)
11x - 9x = 46

Ratnakar said: (Aug 27, 2010)  
Why 9(x-1), it may be 9x-1.

Please explain in detail.

Vinoth said: (Sep 19, 2010)  
No Ratnakar. You are wrong.

Varun said: (Sep 23, 2010)  
Let the average age of 9 members be x.

(x+55)/11 - x/9 = 1

=> x=198.

(198+55)/11 => 23.

Rahul said: (Oct 27, 2010)  
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.

Riya said: (Nov 8, 2010)  
Thanks for the detailed explanation. Now I got it!.

Aditya said: (Nov 24, 2010)  
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

Anand said: (Jan 6, 2011)  
11x - (26 + 29) = 9(x -1) can you explain that how it comes?

Swathy said: (Jan 20, 2011)  
@Anand:
11x(whole team average)-(26+29)(captain+wicket keeper)=9(x-1)(average of 9 players)

here the average age of 9 players age is < the whole team by 1. that is 11x-1=9x.

So we are using 9(x-1).

Panddu said: (Jun 28, 2011)  
11 MEMBERS TEAM PLAYERS AGE OF 26 YEAR OK
1 (ONE) MEMBER IS WICKET KEEPER 3YEARS OLDER THEN REAMING PLAYERS
11-1=10 1 IS WICKET KEEPER
26-3=23

Priya said: (Jul 30, 2011)  
Thanks panddu that was really easy to understand for me.

Vasu said: (Sep 13, 2011)  
One year less than average then why are you using 9x+1? you can use 9x-1 na ?

Abhisshek said: (Oct 13, 2011)  
Let the sum of age of 7 player(excluding captain and keeper)= x
average age of the whole team = (x+26+(26+3))/11 ----eq(1)
average age of a team without captain and keeper = x/9 -----eq(2)

according to the question,
x/9 = (x+26+29)/11 - 1
11x+99=9x+495
x=198
putting the value of x in eq(1) we get,

average age of the whole team = 23years

Mini said: (Dec 30, 2011)  
Good work varun.

M.V.Krishna/Palvoncha said: (Jan 11, 2012)  
Excellent varun.

Sushmita said: (Feb 5, 2012)  
Thanks abhishek.

Palak said: (Feb 13, 2012)  
Can you explain how 29 comes?

M.V.Krishna/Palvoncha said: (Feb 18, 2012)  
@palak

given age of captain is 26yrs.

wicket keeper is 3yrs older than captain.

so we get age of wicket keeper as 26+3=29 yrs.

hope u understood.

Hari said: (Mar 22, 2012)  
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.

Sindhu said: (May 25, 2012)  
As the avg age of remaining when the two persons are excluded is one less than that of avg age of all. Then why +1 is done on the side of avg of remaining after excluding 2 persons ?

Mayur said: (Jun 14, 2012)  
Whole team = X.

11X-55=99-9.

2X=64.

X=23.

Avnish Parashar said: (Jul 23, 2012)  
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

Sowji said: (Jun 2, 2013)  
Sir you are saying that the wicket keeper's age was 29 but in the problem it was not mentioned then how can one take it as 29 years as the age of wicket keeper?

Maddy said: (Aug 6, 2013)  
In question its given 3 years older. It should be clearly given like 3 years older than captain.

Angana said: (Oct 22, 2013)  
"11x - (26 + 29) = 9x - 9" how this 9x - 9 came from? please explain. I don't understand.

Kiki said: (Nov 6, 2013)  
@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.

Vishesh said: (Nov 13, 2013)  
How did you get 9(x-1)? Please explain me.

Vishesh said: (Nov 13, 2013)  
Here the average of 11 members = x.

If two are excluded then average of 9 members is 1 year less than the average of the whole team so = 9(x-1).

Murali said: (Jan 8, 2014)  
Let the average age whole team i.e.
avg = w/11.
w = 11 avg.

If two persons are excluded in the team then the avg is less than 1 of original avg. Therefore,

avg-1 = w-26-29/9.
9avg-9 = 11avg -55 .
2avg = 46.
avg = 23.

Average age of whole team is 23 years.

Bajarang Choudhari said: (Jan 18, 2014)  
Let the Avg. Age = X.
=> 11x-(26+29) = 9(x-1).

=> 11x-55 = 9x-9.
=> 11x-9x = 55-9.

=> 2x = 46.
=> x = 46/2 = 23yrs. answer.

Chander said: (Mar 5, 2014)  
I don't understand the answer please provide me good method for solved it.

Manchala Lakshmanarao said: (Mar 21, 2014)  
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.

Sree said: (May 31, 2014)  
Let x be the avg age.
So x*9 = age of the remaining 9 player.

9x+26+29/11-1 = 9x/9 .......(1).
81x+396 = 99x.
18x = 396.
x = 22.

We need to substitute x valve in eq (1).
So the value is 23.

Faraz Hasan said: (Jun 24, 2014)  
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.

Ram said: (Sep 10, 2014)  
Avg of full team x = (9x9+26+3)/11.
Avg of 9 players x9 = x-1.

x = (9(x-1)+29)/11.
11x = 9x-9+29.
2x = 20.
x = 10.

Average age of whole team is 10 years.

Shilohu said: (Oct 9, 2014)  
As their are 11 members..the average weight = 11 x.

(the average age of the remaining players is one year less than the average age of the whole team).

Remaining players = 9 (as they said exclude captain, keeper).
And their average is less the remaining so it is written as 9(x-1).

Finally,
11 x (total avg weight)-(26+29)(as they asked to exclude) = 9(x-1).

Karthika said: (Oct 30, 2014)  
Age of captain = 26.

Age of wicketkeeper = 29.

Let the sum of ages of remaining players be x.

Now,

x+26+29/11-x/9 = 1.

x = 198.

The average age of players is 198+26+29/11 = 23 years.

Mukesh said: (Feb 3, 2015)  
Let A be average of whole team, so average of 9 members will be (A-1). Now if we take average of Captain, WK and 9 members we should get average of whole team:

So, (26+29+A-1)/3 = A.
Resolving 54+A = 3A.

2A = 54.
A = 27.

Vineela Reddy said: (Feb 7, 2015)  
Let avg of team = x.
Sum = avg*no.of persons.
Sum = x*11.
Let captain age = 26.

Wicketkeeper age = 26+3=29;(3 yrs older than captain so +3 is added).
So now (11x-(26+29)).....eq(1).

Now two are excluded there are 9 members:i.e., N=9;
Given avg is decreased by "-1"so avg is :x-1;

Then sum is=9(x-1).... eqn(2).

Equating 1&2,
We get x=23 years.

Nikhil Verma said: (Mar 9, 2015)  
How does 9(x-1) came? Please make me understand this.

Vardhini said: (Apr 9, 2015)  
x+26+29/11 = Total team average.

Wicket keeper & cap was excluded.

So x+55/11-x/9 = 1 in this comes x value.

So x = 198.

= 198+26+29/11 = 23.

The average of team is 23.

Jeevitha said: (Apr 30, 2015)  
Let the average age of the whole team be x years.

Then, the age of remaining 9 players is 9(x-1).

Given age of captain is 26 years.
Wicket keeper is 3 years older than captain.

So we get age of wicket keeper as 26+3 = 29 years.

Now apply the normal average formula.

{26+29+9 (x-1) }/11 = x.

55+ 9(x-1) = 11x.
9x-9+55 = 11x.

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

Javid Mir said: (May 29, 2015)  
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.

Niranj said: (Jun 26, 2015)  
But I need clear explanation about x/9=(x+26=29/11)-1.

Harsh said: (Aug 7, 2015)  
@Niranjan.

Let x be average of team.

And from question 26 is captain's age and wicket kipper 3 more than captain so it is 29.

And that's why while finding average you may add all the no and divide them by total numbers.

Neha said: (Aug 7, 2015)  
Guys you are so fabulous thank you to explain me all this love this site.

Deepal Joshi said: (Sep 30, 2015)  
Oral solution: Total 55. As they moved out of group remaining elements have given 1 each, means these two have donated 9 in the group. So these two remained with 46.

Average is 23, so initial average is 23.

Sunny said: (Oct 12, 2015)  
Is any body tell me that why we are reducing 1 from average age of 9 persons (x/9-1) ?

In above equation why we reducing that one?

Isak said: (Nov 26, 2015)  
Friends anybody solve this questions in a detailed manner.

Jay Doshi said: (Nov 29, 2015)  
Please explain this sum easily.

Jay Doshi said: (Nov 29, 2015)  
Please explain anybody in details.

Rajeshri said: (Dec 29, 2015)  
I don't understand this problem please explain in details.

Aparichith said: (Dec 31, 2015)  
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.

Rutika said: (Jan 11, 2016)  
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.

Shubham Ln said: (Mar 17, 2016)  
Can't we solve this numerical by, Alligation method?

Mounika Reddy said: (Jun 6, 2016)  
Total 11 members.

So, 10 * 26 + 29 * 1/11 = 26.3.

If two are excluded,

8 * 26 + 29 * 1/11 = 21.6.

Average of team = 26.3 + 21.6/2.

So, the Answer is 23.

Vishal said: (Jul 16, 2016)  
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,

Afzal said: (Jul 25, 2016)  
Total ageaof of 11 player ages 26 = 26 * 11 = 286.
Total of 11 player whose age 29 = 29 * 11 = 319 Difference = 33 average 1 less,
33 - 10 = 23.

Sam said: (Sep 15, 2016)  
I can't understand the question please help anyone.

Monika said: (Oct 14, 2016)  
This method is useful, Thanks @Afzal.

Surya Kiran Sanju said: (Dec 17, 2016)  
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.

Swaroop Teja said: (Jan 20, 2017)  
Here it was so easy, let the age of captain = 26,
wicket keeper = 29.
So, 26 + 29 = 55 forget about this.

Next step: Whole team = 11 members.
Two members excluded so total team members.
Here 11x - 55 = 9(x-1) ---> here x-1 indicates 1year less than the avg age of the whole team.
11x - 55 = 9x-9,
11x - 9x = -9 + 56,
2x = 46,
x = 46/2 = 23.

Ruhi said: (Mar 2, 2017)  
Thanks for explaining @Swaroop.

Jeeny said: (Mar 6, 2017)  
Try this one.

Let, total age of whole team Y.
Then, Y/11 = X.
Y = 11x, x is the average age of the whole team.
Given, Y - (26 + 29)/9 = x-1.
= 11x-55 = 9x-9,
= 2x = 46 = 23.

Achyudha said: (Mar 30, 2017)  
No @Ratnakar

Because 9(x-1)= 9 x (x - 9) x1.
=> 9x-9.

Vikash said: (Jun 19, 2017)  
Let avg age is X.

And out of 11 members two members age is given(C And WC) then remaining players are 9
Let sum of the age of these Players(9) is A
now
X=A+(26+29)/11
A=11X-55------------(1)

And average age of the remaining players after excluded(26+29).
And avg age is 1 year less than,
So
X-1=A/9,
A=9X-9------------------------(2)
solve eqe (1) and (2).
11X-55=9X-9,
2X=46,
x=23.

Rishabh said: (Jun 27, 2017)  
You provide the best and simplest solution, Thanks @Vishal.

Namrata Patil said: (Aug 4, 2017)  
Explained well. Thanks @Kiki.

Sanjana said: (Aug 8, 2017)  
Can you explain how to come 9 (x-1)?

Mehul said: (Aug 8, 2017)  
Explaination:

Number-----------Average -----------Total
11 ----------- x -----------11x
9 ----------- x-1 ----------- 9(x-1).
So, for average of the team :-
11x - (captain + wicketkeeper) = 9(x-1)
hence,
11x - (26+29)=9(x-1),
11x -55 = 9x - 9,
11x - 9x = 46,
2x = 46,
x=23.

Akhil said: (Sep 22, 2017)  
It's very easy.

11 members players age average - WK age.
26 - 3 = 23.

R K said: (Oct 7, 2017)  
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.

Divya said: (Jan 20, 2018)  
How 9 will come can you explain detail?

Chattar Priya said: (Jan 21, 2018)  
Thanks all of you.

Ashwin said: (Mar 19, 2018)  
If we assume c be the avg of the whole team then why 11x-55 why not x-55?

Viji said: (Mar 25, 2018)  
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.

Philo said: (May 12, 2018)  
Can anyone explain using distribution method?

Sowmya said: (Jun 23, 2018)  
why we took 9(x-1) here? Please explain.

Hasritha said: (Jun 27, 2018)  
@Sowmya.

Because rest 9 has 1 year lesser than average of the whole team.

Chiru said: (Aug 10, 2018)  
Thank you @Rahul.

Viswanath Gouda said: (Aug 25, 2018)  
26+29+9(x-1) = 11x,
X=23.

Darshan said: (Sep 26, 2018)  
How it is 9 (x-1)? Please explain.

Vinothini said: (Dec 14, 2018)  
11x-(26+29)=9(x-1),
11x-(55)=9x-9,
11x-9x=55-9,
2x=46,
X=46/2,
X=23years.

Deepa said: (Dec 28, 2018)  
How came 9(x-1)?

Sabitri said: (Feb 1, 2019)  
How come 9 (x-1)? please explain it, I don't understand.

Swapan said: (Mar 9, 2019)  
@Pradeep.

How 9(x-1)? Please explain.

Rohan Kumbhar said: (Mar 15, 2019)  
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.

Adhithya Raj Paul said: (Mar 19, 2019)  
How come 55?

Basit said: (Mar 26, 2019)  
Nice explanation, Thanks @Rohan.

Irfan said: (Apr 29, 2019)  
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.

Gowtham said: (Jun 17, 2019)  
How (x-1) came here?

Anonymous said: (Aug 5, 2019)  
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.

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