A bastman in his 44th innings makes a score of 86 and thereby increases his average by 1. Find the average after 44 innings?

Answer

To solve the problem, we need to find the average score of the batsman after 44 innings, given that he scores 86 in his 44th inning and this increases his average by 1.

### Step-by-Step Solution:

1. **Let the average score after 43 innings be \( x \)**:
- The average score after 43 innings is denoted as \( x \).

2. **Calculate the total score after 43 innings**:
- The total score after 43 innings can be calculated as:
\[ \text{Total score after 43 innings} = 43x \]

3. **Add the score of the 44th inning**:
- The batsman scores 86 in his 44th inning. Therefore, the total score after 44 innings becomes:
\[ \text{Total score after 44 innings} = 43x + 86 \]

4. **Calculate the new average after 44 innings**:
- The new average after 44 innings is given by:
\[ \text{New average} = \frac{\text{Total score after 44 innings}}{44} = \frac{43x + 86}{44} \]

5. **Set up the equation based on the increase in average**:
- According to the problem, the new average is 1 more than the previous average:
\[ \frac{43x + 86}{44} = x + 1 \]

6. **Multiply both sides by 44 to eliminate the fraction**:
\[ 43x + 86 = 44(x + 1) \]

7. **Expand the right side**:
\[ 43x + 86 = 44x + 44 \]

8. **Rearrange the equation**:
\[ 86 - 44 = 44x - 43x \]
\[ 42 = x \]

9. **Conclusion**:
- The average score after 44 innings is \( x + 1 = 42 + 1 = 43 \).

### Final Answer:
The average after 44 innings is **43**.