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Question :

In a cricket team, the average age of eleven players in 28 years. What is the age of the captain?

Statements :

a. The captain is eleven years older than the youngest player.

b. The average age of 10 players, other than the captain is 27.3 years.

c. 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.

A) All a,b and c follows B) Only a and c follows
C) Either b alone or a & b follows D) None

Answer:   C) Either b alone or a & b follows



Explanation:

From statement (b)
Average of 11 players = 11 x 28 = 308
Average of 10 players = 10 x 27.3 = 273
Age of captain = 308 - 273 = 35.

From the Statement (a) we can say that captain's age (C) = y + 11 ...(1) where y-youngers age
From the statement (c),the averge age of 3groups of 3players each was given,
It means total 9 players age was given indirectly,
1st group: 25 x 3 = 75
2nd group: 28 x 3 = 84
3rd group: 30 x 3 = 90
Total  is 75 + 84 + 90 = 249
Now {C + Y + (9 players age sum)}/11 = 28
Y + 11 + Y + (249) = 28 x 11=308
2Y+260=308
2Y = 308-260 = 40 ==> Y=24 ==> C(captain's age)= Y+11 = 24+11 = 35

Therefore, statement b alone or a & c only is the answer.

Subject: Statement and Conclusions
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