Virat has certain batting average of 9 innings . In the tenth innings he scored 106 runs thereby increasing his average by 6 runs . His new batting average is :

Options

A. 48
B. 56
C. 52
D. 46

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Define the variables
Let the original batting average of Virat after 9 innings be \( x \).

### Step 2: Calculate total runs after 9 innings
The total runs scored by Virat in 9 innings can be calculated as:
\[ \text{Total runs in 9 innings} = 9x \]

### Step 3: Include the 10th innings score
In the 10th innings, Virat scored 106 runs. Therefore, the total runs after 10 innings will be:
\[ \text{Total runs in 10 innings} = 9x + 106 \]

### Step 4: Calculate the new average
After scoring 106 runs in the 10th innings, his new average becomes \( x + 6 \). The total number of innings is now 10, so we can express the new average as:
\[ \text{New average} = \frac{9x + 106}{10} \]
Setting this equal to the new average \( x + 6 \):
\[ \frac{9x + 106}{10} = x + 6 \]

### Step 5: Clear the fraction
To eliminate the fraction, multiply both sides by 10:
\[ 9x + 106 = 10(x + 6) \]

### Step 6: Expand the equation
Expanding the right side gives:
\[ 9x + 106 = 10x + 60 \]

### Step 7: Rearrange the equation
Now, rearranging the equation to isolate \( x \):
\[ 9x + 106 - 60 = 10x \]
\[ 9x + 46 = 10x \]

### Step 8: Solve for \( x \)
Subtract \( 9x \) from both sides:
\[ 46 = 10x - 9x \]
\[ 46 = x \]

### Step 9: Find the new average
Now that we have \( x \), we can find the new average:
\[ \text{New average} = x + 6 = 46 + 6 = 52 \]

### Final Answer
Thus, Virat's new batting average is \( \boxed{52} \).

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