The average age of eleven players of a cricket team decreases by 2 months when two new players are included in the team replacing two players of age 17 years and 20 years. The average age of new player is

Options

A. 17 years 1 month
B. 17 years 7 months
C. 17 years 11 months
D. 18 years 3 months

Answer

To solve the problem, we need to find the average age of the two new players who replace the two players aged 17 years and 20 years.

### Step-by-Step Solution:

1. **Calculate the total age of the original 11 players.**
Let the average age of the original 11 players be \( A \) years.
Therefore, the total age of the original 11 players is:
\[ \text{Total age of 11 players} = 11A \]

2. **Determine the new average age after replacing the players.**
The average age decreases by 2 months when the two new players are included. Since 2 months is \(\frac{2}{12} = \frac{1}{6}\) years, the new average age becomes:
\[ A - \frac{1}{6} \]

3. **Calculate the total age of the new team of 11 players.**
After including the two new players, the total age of the new team becomes:
\[ \text{Total age of new team} = 11 \left( A - \frac{1}{6} \right) = 11A - \frac{11}{6} \]

4. **Account for the ages of the replaced players.**
The two players aged 17 years and 20 years are replaced, so the total age of the replaced players is:
\[ 17 + 20 = 37 \text{ years} \]

5. **Set up the equation for the total age of the new team.**
The total age of the new team can also be expressed as the total age of the original players minus the ages of the two replaced players plus the ages of the two new players (let's denote the average age of the new players as \( x \)):
\[ 11A - 37 + 2x = 11A - \frac{11}{6} \]

6. **Simplify the equation.**
By simplifying the equation, we can eliminate \( 11A \) from both sides:
\[ -37 + 2x = -\frac{11}{6} \]

7. **Solve for \( x \).**
Rearranging gives:
\[ 2x = -\frac{11}{6} + 37 \]
Convert 37 into a fraction with a denominator of 6:
\[ 37 = \frac{222}{6} \]
Now substituting:
\[ 2x = \frac{222}{6} - \frac{11}{6} = \frac{211}{6} \]
Dividing both sides by 2:
\[ x = \frac{211}{12} \]

8. **Convert \( x \) into years and months.**
To convert \( \frac{211}{12} \) years into years and months:
\[ x = 17 \text{ years and } \frac{7}{12} \text{ of a year} \approx 17 \text{ years and } 7 \text{ months} \]

### Final Answer:
The average age of the two new players is approximately **17 years and 7 months**.