The bowling average of a bowler is 12.4. He took 5 wickets for 26 runs in his last match then his average improves by 0.4. Find the number of wickets before last match.

Answer

To solve the problem, we will follow these steps:

1. **Understand the given information**:
- The bowler's initial average is 12.4.
- He took 5 wickets for 26 runs in his last match.
- His average improves by 0.4 after this match.

2. **Define variables**:
- Let \( X \) be the number of wickets the bowler had taken before the last match.

3. **Calculate the total runs conceded before the last match**:
- The total runs conceded by the bowler before the last match can be calculated using the formula for bowling average:
\[ \text{Total Runs Conceded} = \text{Bowling Average} \times \text{Number of Wickets} \]
- Therefore, the runs conceded before the last match is:
\[ \text{Total Runs} = 12.4 \times X \]

4. **Calculate the total runs conceded after the last match**:
- After taking 5 wickets for 26 runs, the total runs conceded becomes:
\[ \text{Total Runs After Last Match} = 12.4X + 26 \]

5. **Calculate the total number of wickets after the last match**:
- The total number of wickets after the last match is:
\[ \text{Total Wickets} = X + 5 \]

6. **Set up the equation for the new average**:
- The new average after the last match is given as:
\[ \text{New Average} = 12.4 - 0.4 = 12 \]
- Therefore, we can set up the equation:
\[ \frac{12.4X + 26}{X + 5} = 12 \]

7. **Cross-multiply to solve for \( X \)**:
- Cross-multiplying gives:
\[ 12.4X + 26 = 12(X + 5) \]
- Expanding the right side:
\[ 12.4X + 26 = 12X + 60 \]

8. **Rearranging the equation**:
- Move all terms involving \( X \) to one side and constant terms to the other:
\[ 12.4X - 12X = 60 - 26 \]
- This simplifies to:
\[ 0.4X = 34 \]

9. **Solve for \( X \)**:
- Dividing both sides by 0.4 gives:
\[ X = \frac{34}{0.4} = 85 \]

10. **Conclusion**:
- The number of wickets the bowler had taken before the last match is \( 85 \).