Aptitude - Average - Discussion
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
In a cricket team, the average age of eleven players in 28 years. What is the age of the captain? | |
I. | The captain is eleven years older than the youngest player. |
II. | The average age of 10 players, other than the captain is 27.3 years. |
III. | Leaving aside the captain and the youngest player, the average ages of three groups of three players each are 25 years, 28 years and 30 years respectively. |
Total age of 11 players = (28 x 11) years = 308 years.
I. C = Y + 11 
C - Y = 11 .... (i)
II. Total age of 10 players (excluding captain) = (27.3 x 10) years = 273 years.
Age of captain = (308 - 273) years = 35 years.
Thus, C = 35. .... (ii)
From (i) and (ii), we get Y = 24
III. Total age of 9 players = [ (25 x 3) + (28 x 3) + (30 x 3)] years = 249 years.
C + Y = (308 - 249) = 59 .... (iii)
From (i) and (iii), we get C = 35.
Thus, II alone gives the answer.
Also, I and III together give the answer.
Correct answer is (C).
From (1);
c+11=y. Then c-y=11---> eqn(1).
From (3)---
3(25)+3(28)+3(30)+c+y = 308.
75+84+90+c+y = 308.
c+y=308-249.
c+y=59 --> eqn(2).
From eqn 1&2.
c-y = 11.
c+y = 59.
----------
2c =70.
Therefore, c=35.
Given in the question Average age of 11 players = 28 years.
By applying average formula, Average = total / Number of items,
28 = total / 11 => total = 28 x 11 => 308.
II. The average age of 10 players, other than the captain is 27.3 years.
By applying the average formula, Average = (total - x) / Number of items [Average is calculated without the captain's age. So subtracting captain's age from total].
27.3 = (308 - x) / 10 => 308 - x = 273.
Therefore, x = 35. Captain's Age.
C+y=59
C-y=11
_______
C=48.
Please anyone explain it.
The answer should be 2 only.
Please explain this in clearly.
In 1 we have equation C - Y = 11 and in 3 equation is C + Y = 59. Solve those two equations so that we can get captain age.