Aptitude - Average - Discussion

Discussion Forum : Average - Data Sufficiency 2 (Q.No. 2)
Directions to Solve

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.


2.

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.

Any two of the three
All I, II and III
II only or I and III only
II and III only
None of these
Answer: Option
Explanation:

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).

Discussion:
13 comments Page 2 of 2.

Bindiya Shetty said:   5 years ago
From 1&3 I got c = 48.

C+y=59
C-y=11
_______
C=48.

Please anyone explain it.
(2)

Atom said:   5 years ago
II is enough to find Captain's age.

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.

Hari said:   4 years ago
1 and 3 is also sufficient;

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.


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