The bowling average of a cricketer was 12.4. He decreases his average by 0.2 points when he takes 5 wickets for 26 runs in his last match . The number of wickets taken by him before the last match was

Options

A. 125
B. 150
C. 175
D. 200

Answer

To solve the problem, we need to determine the number of wickets taken by the cricketer before his last match, given that his bowling average decreased after taking 5 wickets for 26 runs.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Initial bowling average = 12.4
- Decrease in average = 0.2
- Wickets taken in the last match = 5
- Runs given in the last match = 26

2. **Calculate the New Bowling Average:**
- New bowling average after the last match = 12.4 - 0.2 = 12.2

3. **Let the Number of Wickets Before the Last Match be \( p \):**
- Total wickets after the last match = \( p + 5 \)
- Total runs given before the last match = \( 12.4 \times p \) (since average = total runs / total wickets)

4. **Calculate Total Runs After the Last Match:**
- Total runs after the last match = Total runs before last match + Runs in last match
- Total runs after the last match = \( 12.4p + 26 \)

5. **Set Up the Equation Using the New Average:**
- The new average can be expressed as:
\[ \frac{12.4p + 26}{p + 5} = 12.2 \]

6. **Cross-Multiply to Eliminate the Fraction:**
\[ 12.4p + 26 = 12.2(p + 5) \]

7. **Expand the Right Side:**
\[ 12.4p + 26 = 12.2p + 61 \]

8. **Rearrange the Equation:**
- Move all terms involving \( p \) to one side and constant terms to the other side:
\[ 12.4p - 12.2p = 61 - 26 \]
\[ 0.2p = 35 \]

9. **Solve for \( p \):**
\[ p = \frac{35}{0.2} = 175 \]

10. **Conclusion:**
- The number of wickets taken by the cricketer before the last match is \( p = 175 \).

### Final Answer:
The number of wickets taken by him before the last match was **175**.