A batsman in his `17^(th)` innings makes a score of 85, and thereby increases his average by 3. What is his average after 17 innings?

Answer

To solve the problem, we will follow these steps:

1. **Define the Variables**: Let the average score after 16 innings be \( x \).

2. **Calculate Total Score for 16 Innings**: The total score after 16 innings can be calculated as:
\[ \text{Total score after 16 innings} = 16x \]

3. **Add the 17th Innings Score**: The batsman scores 85 in his 17th innings, so the total score after 17 innings becomes:
\[ \text{Total score after 17 innings} = 16x + 85 \]

4. **Calculate New Average**: The new average after 17 innings will be:
\[ \text{New average} = \frac{16x + 85}{17} \]

5. **Set Up the Equation**: According to the problem, the new average is 3 more than the previous average \( x \):
\[ \frac{16x + 85}{17} = x + 3 \]

6. **Clear the Fraction**: Multiply both sides by 17 to eliminate the fraction:
\[ 16x + 85 = 17(x + 3) \]

7. **Expand the Right Side**: Distributing on the right side gives:
\[ 16x + 85 = 17x + 51 \]

8. **Rearrange the Equation**: Move all terms involving \( x \) to one side and constant terms to the other:
\[ 85 - 51 = 17x - 16x \]
\[ 34 = x \]

9. **Conclusion**: The average after 17 innings is:
\[ x + 3 = 34 + 3 = 37 \]

Thus, the average after 17 innings is **37**.