A cricketer whose bowling average is 12.4 runs per wicket, takes 5 wickets for 26 runs and there by decreases his average by 0.4. Find out the number of wickets taken by him till the last match.

Options

A. 75
B. 81
C. 85
D. 79

Answer

To solve the problem step by step, we will use the information given about the cricketer's bowling average, the number of wickets taken, and the runs conceded.

### Step 1: Define Variables
Let \( n \) be the number of wickets taken by the cricketer before the last match.

### Step 2: Calculate Total Runs Conceded Before the Last Match
The cricketer's bowling average before the last match is 12.4 runs per wicket. Therefore, the total runs conceded before the last match can be calculated as:
\[ \text{Total runs conceded} = \text{Average} \times \text{Number of wickets} = 12.4 \times n \]

### Step 3: Calculate New Average After Last Match
After taking 5 wickets for 26 runs in the last match, the cricketer's new average decreases by 0.4. Therefore, the new average is:
\[ \text{New Average} = 12.4 - 0.4 = 12.0 \]

### Step 4: Calculate Total Wickets After Last Match
After the last match, the total number of wickets taken becomes:
\[ \text{Total wickets} = n + 5 \]

### Step 5: Calculate Total Runs Conceded After Last Match
After the last match, the total runs conceded becomes:
\[ \text{Total runs conceded} = \text{Total runs before last match} + \text{Runs in last match} = 12.4n + 26 \]

### Step 6: Set Up the Equation Using the New Average
Using the new average, we can set up the equation:
\[ \text{New Average} = \frac{\text{Total runs conceded}}{\text{Total wickets}} \]
Substituting the values we have:
\[ 12.0 = \frac{12.4n + 26}{n + 5} \]

### Step 7: Solve the Equation
Now, we will cross-multiply to solve for \( n \):
\[ 12.0(n + 5) = 12.4n + 26 \]
Expanding both sides:
\[ 12.0n + 60 = 12.4n + 26 \]
Rearranging the equation:
\[ 60 - 26 = 12.4n - 12.0n \]
\[ 34 = 0.4n \]
Dividing both sides by 0.4:
\[ n = \frac{34}{0.4} = 85 \]

### Step 8: Conclusion
The number of wickets taken by the cricketer till the last match is \( n + 5 = 85 + 5 = 90 \). However, since the question asks for wickets taken before the last match, the answer is:
\[ \text{Wickets taken before the last match} = 85 \]