The average age of a cricket team of 11 players is the same as it was 3 years back because 3 of the players whose current average age of 33 years were replaced by 3 youngsters. The average age of the newcomers is

Options

A. 23 years
B. 21 years
C. 22 years
D. 20 years

Answer

To solve the problem, we need to find the average age of the newcomers who replaced the three players in the cricket team.

### Step-by-Step Solution:

1. **Understanding the Current Average Age**:
Let's denote the average age of the cricket team 3 years ago as \( A \). Since the average age of the team remains the same now as it was 3 years ago, we can say that the current average age of the team is also \( A \).

2. **Calculating the Total Age of the Team 3 Years Ago**:
The total age of the team 3 years ago can be calculated as:
\[ \text{Total age 3 years ago} = A \times 11 \]

3. **Calculating the Total Age of the Team Now**:
Each player has aged 3 years since then, so the total age of the team now is:
\[ \text{Total age now} = (A + 3) \times 11 \]

4. **Setting Up the Equation**:
Since the average age has remained the same, we can set the total ages equal to each other:
\[ A \times 11 = (A + 3) \times 11 - \text{Total age of the 3 replaced players} + \text{Total age of the 3 newcomers} \]

5. **Calculating the Total Age of the Replaced Players**:
The three players who were replaced have an average age of 33 years. Therefore, their total age is:
\[ \text{Total age of replaced players} = 3 \times 33 = 99 \]

6. **Substituting Values**:
Now we can substitute the total age of the replaced players into the equation:
\[ A \times 11 = (A + 3) \times 11 - 99 + \text{Total age of the 3 newcomers} \]

7. **Simplifying the Equation**:
Rearranging gives us:
\[ \text{Total age of the 3 newcomers} = A \times 11 - (A + 3) \times 11 + 99 \]
\[ = -3 \times 11 + 99 = -33 + 99 = 66 \]

8. **Finding the Average Age of the Newcomers**:
The average age of the 3 newcomers can be calculated as:
\[ \text{Average age of newcomers} = \frac{\text{Total age of the newcomers}}{3} = \frac{66}{3} = 22 \]

### Final Answer:
The average age of the newcomers is **22 years**.