A cricketer whose bowling average is 24.85, runs per wicket, takes 5 wickets for 52 runs and thereby decreases his average by 0.85. The number of wickets taken by him till the last match was :

Options

A. 64
B. 72
C. 80
D. 96

Answer

To solve the problem, we will follow these steps:

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

### Step 2: Calculate Initial Runs
The cricketer's bowling average is given as 24.85 runs per wicket. Therefore, the total runs conceded by the cricketer before the last match can be calculated as:
\[ \text{Total Runs} = \text{Average} \times \text{Wickets} = 24.85 \times x \]

### Step 3: Update Wickets and Runs After Last Match
After taking 5 wickets for 52 runs, the total number of wickets becomes \( x + 5 \) and the total runs become:
\[ \text{Total Runs After Last Match} = 24.85x + 52 \]

### Step 4: Calculate New Average
The new average after the last match is:
\[ \text{New Average} = \frac{\text{Total Runs After Last Match}}{\text{Total Wickets After Last Match}} = \frac{24.85x + 52}{x + 5} \]
According to the problem, this new average is 0.85 less than the previous average:
\[ \text{New Average} = 24.85 - 0.85 = 24 \]

### Step 5: Set Up the Equation
Now, we can set up the equation:
\[ \frac{24.85x + 52}{x + 5} = 24 \]

### Step 6: Cross Multiply to Solve for \( x \)
Cross-multiplying gives:
\[ 24.85x + 52 = 24(x + 5) \]
Expanding the right side:
\[ 24.85x + 52 = 24x + 120 \]

### Step 7: Rearranging the Equation
Now, rearranging the equation to isolate \( x \):
\[ 24.85x - 24x = 120 - 52 \]
\[ 0.85x = 68 \]

### Step 8: Solve for \( x \)
Dividing both sides by 0.85:
\[ x = \frac{68}{0.85} = 80 \]

### Conclusion
Thus, the number of wickets taken by the cricketer till the last match was \( \boxed{80} \).

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