A batsman makes a score of 87 runs In the 17th Innings and thus Increased his average by 3. Find his average after 17th innings.

Options

A. 39
B. 87
C. 90
D. 84

Answer

To solve the problem step by step, let's break down the information provided and calculate the average after the 17th innings.

### Step-by-Step Solution:

1. **Understand the Problem**:
- A batsman scores 87 runs in his 17th innings.
- This score increases his average by 3 runs.

2. **Let’s Define Variables**:
- Let the average score after 16 innings be \( x \).
- Therefore, the average after 17 innings will be \( x + 3 \).

3. **Calculate Total Runs**:
- The total runs scored in the first 16 innings can be expressed as \( 16x \).
- After scoring 87 runs in the 17th innings, the total runs after 17 innings will be \( 16x + 87 \).

4. **Set Up the Average Equation**:
- The average after 17 innings can also be expressed as:
\[ \text{Average after 17 innings} = \frac{\text{Total runs after 17 innings}}{17} = \frac{16x + 87}{17} \]
- According to the problem, this average is also equal to \( x + 3 \).

5. **Create the Equation**:
- We can set up the equation:
\[ \frac{16x + 87}{17} = x + 3 \]

6. **Clear the Fraction**:
- Multiply both sides by 17 to eliminate the fraction:
\[ 16x + 87 = 17(x + 3) \]

7. **Expand the Right Side**:
- Expanding gives:
\[ 16x + 87 = 17x + 51 \]

8. **Rearrange the Equation**:
- Rearranging terms gives:
\[ 87 - 51 = 17x - 16x \]
\[ 36 = x \]

9. **Find the Average After 17 Innings**:
- Now that we have \( x = 36 \), we can find the average after 17 innings:
\[ \text{Average after 17 innings} = x + 3 = 36 + 3 = 39 \]

### Final Answer:
The average after the 17th innings is **39**.