A batsman in his 10th inning makes a score of 48 runs and thereby increases his average score by 3. What is his average after the 10th inning?

Options

A. 21
B. 20
C. 22
D. None of these

Answer

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

### Step 1: Define the average score before the 10th inning
Let the average score of the batsman after 9 innings be \( x \).

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

### Step 3: Determine the new average after the 10th inning
After scoring 48 runs in the 10th inning, the batsman's average increases by 3. Therefore, the new average after the 10th inning can be expressed as:
\[ \text{New average} = x + 3 \]

### Step 4: Calculate the total runs after 10 innings
The total runs after 10 innings will be the total runs from the first 9 innings plus the runs scored in the 10th inning:
\[ \text{Total runs after 10 innings} = 9x + 48 \]

### Step 5: Set up the equation for the new average
The new average after 10 innings can also be expressed as:
\[ \text{New average} = \frac{\text{Total runs after 10 innings}}{\text{Number of innings}} = \frac{9x + 48}{10} \]

### Step 6: Set the two expressions for the new average equal to each other
We can set the two expressions for the new average equal to each other:
\[ x + 3 = \frac{9x + 48}{10} \]

### Step 7: Solve the equation
To eliminate the fraction, multiply both sides by 10:
\[ 10(x + 3) = 9x + 48 \]
This simplifies to:
\[ 10x + 30 = 9x + 48 \]
Now, isolate \( x \) by subtracting \( 9x \) from both sides:
\[ 10x - 9x + 30 = 48 \]
This simplifies to:
\[ x + 30 = 48 \]
Now, subtract 30 from both sides:
\[ x = 48 - 30 \]
Thus, we find:
\[ x = 18 \]

### Step 8: Calculate the new average after the 10th inning
Now that we have \( x \), we can find the new average after the 10th inning:
\[ \text{New average} = x + 3 = 18 + 3 = 21 \]

### Final Answer
The average score of the batsman after the 10th inning is \( \boxed{21} \).

---