A batsman scores 92 runs in the inning and thus increases his average by 4. What is his average after the inning?

Options

A. 40
B. 32
C. 35
D. Can't be Determined

Answer

To solve the problem, we need to determine the batsman's average after scoring 92 runs, given that this score increases his average by 4 runs. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( n \) = number of innings played before scoring 92 runs
- \( x \) = average runs scored before scoring 92 runs

### Step 2: Calculate Total Runs Before the Innings
The total runs scored before the innings can be expressed as:
\[ \text{Total runs before} = n \cdot x \]

### Step 3: Calculate New Average After Scoring 92 Runs
After scoring 92 runs, the batsman has played \( n + 1 \) innings. The new total runs will be:
\[ \text{Total runs after} = n \cdot x + 92 \]
The new average after scoring 92 runs is:
\[ \text{New average} = \frac{n \cdot x + 92}{n + 1} \]

### Step 4: Set Up the Equation for the Increase in Average
According to the problem, the new average is 4 runs more than the old average:
\[ \frac{n \cdot x + 92}{n + 1} = x + 4 \]

### Step 5: Cross Multiply to Eliminate the Fraction
Cross multiplying gives us:
\[ n \cdot x + 92 = (x + 4)(n + 1) \]

### Step 6: Expand the Right Side
Expanding the right side:
\[ n \cdot x + 92 = n \cdot x + x + 4n + 4 \]

### Step 7: Simplify the Equation
Subtract \( n \cdot x \) from both sides:
\[ 92 = x + 4n + 4 \]
Rearranging gives:
\[ x + 4n = 88 \]

### Step 8: Determine the Average After the Innings
Now, we need to express the new average:
\[ \text{New average} = x + 4 \]
From the equation \( x + 4n = 88 \), we can express \( x \):
\[ x = 88 - 4n \]
Substituting this into the new average:
\[ \text{New average} = (88 - 4n) + 4 = 92 - 4n \]

### Step 9: Conclusion
Since we do not have a specific value for \( n \) (the number of innings played before), we cannot determine a specific numerical value for the new average. Therefore, the answer is:

**Cannot be determined.**