Average age of a team having 12 players is 23 years. If the age of the coach is also included, then the average age increases by 2 years. What is the age (in years) of the coach ?

Options

A. 41
B. 47
C. 49
D. 51

Answer

To solve the problem step by step, we can follow these calculations:

1. **Calculate the total age of the 12 players.**
- Given that the average age of the 12 players is 23 years, we can find the total age using the formula:
\[ \text{Total age of players} = \text{Average age} \times \text{Number of players} \]
- Therefore:
\[ \text{Total age of players} = 23 \times 12 = 276 \text{ years} \]

2. **Determine the new average age when the coach is included.**
- The problem states that when the coach's age is included, the average age increases by 2 years. Thus, the new average age becomes:
\[ \text{New average age} = 23 + 2 = 25 \text{ years} \]

3. **Set up the equation for the new average age including the coach.**
- When the coach is included, the total number of individuals becomes 13 (12 players + 1 coach). The formula for the new average age is:
\[ \text{New average} = \frac{\text{Total age of players} + \text{Coach's age}}{\text{Total number of individuals}} \]
- Plugging in the values we have:
\[ 25 = \frac{276 + \text{Coach's age}}{13} \]

4. **Solve for the coach's age.**
- To eliminate the fraction, multiply both sides by 13:
\[ 25 \times 13 = 276 + \text{Coach's age} \]
- Calculate \(25 \times 13\):
\[ 25 \times 13 = 325 \]
- Now we have:
\[ 325 = 276 + \text{Coach's age} \]
- Rearranging gives us:
\[ \text{Coach's age} = 325 - 276 \]
- Therefore:
\[ \text{Coach's age} = 49 \text{ years} \]

5. **Conclusion.**
- The age of the coach is 49 years.