Aptitude - Average - Discussion
Discussion Forum : Average - General Questions (Q.No. 6)
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?
Answer: Option
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.
Discussion:
129 comments Page 9 of 13.
Vishal said:
9 years ago
For the answer to question how 9 (x-1) came?
Let x be the Avg of the whole team5.
(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,
Let x be the Avg of the whole team
(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:
9 years ago
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.
Total of 11 player whose age 29 = 29 * 11 = 319 Difference = 33 average 1 less,
33 - 10 = 23.
Sam said:
9 years ago
I can't understand the question please help anyone.
Monika said:
9 years ago
This method is useful, Thanks @Afzal.
Swaroop teja said:
9 years ago
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.
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:
9 years ago
Thanks for explaining @Swaroop.
Jeeny said:
9 years ago
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.
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:
8 years ago
No @Ratnakar
Because 9(x-1)= 9 x (x - 9) x1.
=> 9x-9.
Because 9(x-1)= 9 x (x - 9) x1.
=> 9x-9.
Vikash said:
8 years ago
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.
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:
8 years ago
You provide the best and simplest solution, Thanks @Vishal.
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