The captain of a cricket team of 11 members is 26 years old, and the wicket-keeper is three years older than the captain. If the ages of captain and wicketkeeper are excluded, the average age of the remaining players of the team is one year less than the average age of the whole team. What is the average age of the team?

Options

A. 23
B. 17
C. 49
D. 19

Answer

To solve the problem step by step, let's denote the average age of the whole team as \( Y \).

### Step 1: Define the total age of the team
The cricket team consists of 11 members. If the average age of the whole team is \( Y \), then the total age \( X \) of the team can be expressed as:
\[ X = 11Y \]
**Hint:** Remember that the total age is the average age multiplied by the number of members.

### Step 2: Determine the ages of the captain and wicket-keeper
The captain's age is given as 26 years. The wicket-keeper is 3 years older than the captain, so:
\[ \text{Wicket-keeper's age} = 26 + 3 = 29 \text{ years} \]

### Step 3: Calculate the total age of the remaining players
When we exclude the ages of the captain and the wicket-keeper, the total age of the remaining 9 players is:
\[ \text{Total age of remaining players} = X - 26 - 29 = 11Y - 55 \]

### Step 4: Find the average age of the remaining players
The average age of the remaining players can be calculated as:
\[ \text{Average age of remaining players} = \frac{11Y - 55}{9} \]

### Step 5: Set up the equation based on the problem statement
According to the problem, the average age of the remaining players is one year less than the average age of the whole team. Therefore, we can set up the equation:
\[ \frac{11Y - 55}{9} = Y - 1 \]

### Step 6: Solve the equation
Now, we will solve the equation for \( Y \):
1. Multiply both sides by 9 to eliminate the fraction:
\[ 11Y - 55 = 9(Y - 1) \]
2. Expand the right side:
\[ 11Y - 55 = 9Y - 9 \]
3. Rearranging gives:
\[ 11Y - 9Y = 55 - 9 \]
\[ 2Y = 46 \]
4. Divide both sides by 2:
\[ Y = 23 \]

### Conclusion
The average age of the whole team is:
\[ \boxed{23} \text{ years} \]