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 step-by-step, we can follow these calculations:

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

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

### Step 3: Add Runs Conceded in the Last Match
In the last match, he took 5 wickets and conceded 52 runs. Thus, the new total runs after the last match becomes:
\[ \text{New Total Runs} = 24.85x + 52 \]

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

### Step 5: Calculate New Average
The new average after the last match is given to decrease by 0.85:
\[ \text{New Average} = 24.85 - 0.85 = 24 \]

### Step 6: Set Up the Equation for the New Average
Using the formula for average, we can set up the equation:
\[ \frac{24.85x + 52}{x + 5} = 24 \]

### Step 7: Cross-Multiply to Solve the Equation
Cross-multiplying gives us:
\[ 24.85x + 52 = 24(x + 5) \]
Expanding the right side:
\[ 24.85x + 52 = 24x + 120 \]

### Step 8: Rearrange the Equation
Rearranging gives:
\[ 24.85x - 24x = 120 - 52 \]
\[ 0.85x = 68 \]

### Step 9: Solve for \( x \)
Now, divide both sides by 0.85:
\[ x = \frac{68}{0.85} \]
To simplify, multiply numerator and denominator by 100:
\[ x = \frac{6800}{85} = 80 \]

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

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