The age of the captain of a cricket team of 11 players is 25 years and the wicket keeper is 3 years older than the captain. If the ages of these two are excluded, the average age of the remaining players of the team becomes 1 year less than the average age of the whole team. what is the average age of the whole team ?

Options

A. 18 years
B. 22 years
C. 25 years
D. 23 years

Answer

To find the average age of the whole cricket team, let's break down the problem step by step.

### Step 1: Define Variables
Let the average age of the whole team be \( x \) years.

### Step 2: Determine Ages of Captain and Wicketkeeper
- The age of the captain is given as 25 years.
- The wicketkeeper is 3 years older than the captain, so:
\[ \text{Age of Wicketkeeper} = 25 + 3 = 28 \text{ years} \]

### Step 3: Calculate Total Age of the Team
The total number of players in the team is 11. Therefore, the total age of the team can be expressed as:
\[ \text{Total Age of Team} = 11x \]

### Step 4: Exclude Ages of Captain and Wicketkeeper
When we exclude the ages of the captain and the wicketkeeper, the total age of the remaining 9 players is:
\[ \text{Total Age of Remaining Players} = 11x - (25 + 28) = 11x - 53 \]

### Step 5: Determine Average Age of Remaining Players
The average age of the remaining 9 players is given as:
\[ \text{Average Age of Remaining Players} = \frac{11x - 53}{9} \]

### Step 6: Set Up the Equation
According to the problem, the average age of the remaining players is 1 year less than the average age of the whole team:
\[ \frac{11x - 53}{9} = x - 1 \]

### Step 7: Cross-Multiply to Solve for \( x \)
Cross-multiplying gives:
\[ 11x - 53 = 9(x - 1) \]
Expanding the right side:
\[ 11x - 53 = 9x - 9 \]

### Step 8: Rearranging the Equation
Now, we can rearrange the equation:
\[ 11x - 9x = -9 + 53 \]
This simplifies to:
\[ 2x = 44 \]

### Step 9: Solve for \( x \)
Dividing both sides by 2:
\[ x = 22 \]

### Conclusion
The average age of the whole team is:
\[ \text{Average Age of the Whole Team} = 22 \text{ years} \]