A cricketer, whose bowling average was 12.4 runs/wicket takes 5 wickets for 22 runs in a match, thereby decreases his average by 0.4. The number of wickets, taken by him before this match was :

Options

A. 78
B. 87
C. 95
D. 105

Answer

To solve the problem step-by-step, we can follow these steps:

### Step 1: Understand the given information
The cricketer's initial bowling average is 12.4 runs per wicket. After taking 5 wickets for 22 runs in a match, his average decreases by 0.4.

### Step 2: Calculate the new average
The new average after the match will be:
\[ \text{New Average} = \text{Old Average} - 0.4 = 12.4 - 0.4 = 12.0 \text{ runs/wicket} \]

### Step 3: Set up the equation for the average
Let \( n \) be the number of wickets taken before the last match. The total runs given before the last match can be calculated using the formula for average:
\[ \text{Total Runs} = \text{Average} \times \text{Number of Wickets} \]
Thus, before the last match:
\[ \text{Total Runs} = 12.4n \]

After the match, he took 5 more wickets, so the total number of wickets becomes \( n + 5 \). The total runs given after the match will be:
\[ \text{Total Runs after match} = 12.4n + 22 \]

### Step 4: Set up the new average equation
Now, using the new average:
\[ \text{New Average} = \frac{\text{Total Runs after match}}{\text{Total Wickets after match}} \]
Substituting the values we have:
\[ 12.0 = \frac{12.4n + 22}{n + 5} \]

### Step 5: Solve the equation
Cross-multiplying gives us:
\[ 12.0(n + 5) = 12.4n + 22 \]
Expanding both sides:
\[ 12.0n + 60 = 12.4n + 22 \]
Rearranging the equation:
\[ 60 - 22 = 12.4n - 12.0n \]
\[ 38 = 0.4n \]
Now, solving for \( n \):
\[ n = \frac{38}{0.4} = 95 \]

### Conclusion
The number of wickets taken by him before this match was **95**.

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