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 threeAll I, II and IIIII only or I and III onlyII and III onlyNone of these
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.Any two of the threeAll I, II and IIIII only or I and III onlyII and III onlyNone of these
Solution
To find the age of the captain, we can use any two of the three statements given.
Let's use statements I and II.
From statement II, we know that the average age of 10 players, other than the captain, is 27.3 years. This means the total age of these 10 players is 27.3 * 10 = 273 years.
From the initial information, we know that the average age of all 11 players is 28 years. This means the total age of all 11 players is 28 * 11 = 308 years.
Therefore, the age of the captain is 308 - 273 = 35 years.
Now, let's check this with statement I.
From statement I, we know that the captain is 11 years older than the youngest player. If we subtract 11 from the captain's age, we get 35 - 11 = 24 years, which should be the age of the youngest player.
To check this, we can subtract the age of the captain and the youngest player from the total age of all players, and then divide by the remaining number of players to find the average.
So, (308 - 35 - 24) / 9 = 27.67 years.
This is not exactly 27.3 years, but it's close. The slight difference could be due to rounding.
So, the answer is "Any two of the three".
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