A batsman makes a score of 58 runs in the 15th innings and thus increases his average by 3 runs. What is the average after 15th innings ?

Options

A. 12
B. 14
C. 16
D. 18

Answer

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

### Step 1: Define the average before the 15th innings
Let the average score of the batsman after 14 innings be \( x \).

### Step 2: Determine the new average after the 15th innings
According to the problem, after scoring 58 runs in the 15th innings, the batsman's average increases by 3 runs. Therefore, the new average after 15 innings will be \( x + 3 \).

### Step 3: Set up the equation
The total runs scored after 14 innings can be expressed as \( 14x \). After the 15th innings, the total runs scored will be \( 14x + 58 \). The average after 15 innings can also be expressed as:

\[ \text{New Average} = \frac{\text{Total Runs}}{\text{Number of Innings}} = \frac{14x + 58}{15} \]

### Step 4: Equate the two expressions for the new average
We can set up the equation:

\[ \frac{14x + 58}{15} = x + 3 \]

### Step 5: Clear the fraction by multiplying both sides by 15
Multiplying both sides by 15 gives:

\[ 14x + 58 = 15(x + 3) \]

### Step 6: Expand the right side
Expanding the right side results in:

\[ 14x + 58 = 15x + 45 \]

### Step 7: Rearrange the equation to isolate \( x \)
Now, we can rearrange the equation:

\[ 14x + 58 - 45 = 15x \]
\[ 14x + 13 = 15x \]

### Step 8: Solve for \( x \)
Subtract \( 14x \) from both sides:

\[ 13 = 15x - 14x \]
\[ 13 = x \]

### Step 9: Calculate the new average
Now that we have \( x = 13 \), we can find the new average after the 15th innings:

\[ \text{New Average} = x + 3 = 13 + 3 = 16 \]

### Conclusion
The average after the 15th innings is **16**.

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