A batsman makes a score of 81 runs in the 16th match and thus Increases his average runs per match by 3. What Is his average after the 16th match?

Options

A. 35
B. 34
C. 33
D. 36

Answer

To solve the problem, we need to find the average runs scored by the batsman after the 16th match, given that his score in the 16th match is 81 runs and that this score increases his average by 3 runs per match.

### Step-by-Step Solution:

1. **Let the average runs after 15 matches be \( x \)**:
- The average runs scored by the batsman before the 16th match is denoted as \( x \).

2. **Calculate the total runs scored in the first 15 matches**:
- The total runs scored in the first 15 matches can be calculated as:
\[ \text{Total runs in 15 matches} = 15x \]

3. **Calculate the total runs after the 16th match**:
- After scoring 81 runs in the 16th match, the total runs become:
\[ \text{Total runs after 16 matches} = 15x + 81 \]

4. **Calculate the new average after 16 matches**:
- The new average after 16 matches is given by:
\[ \text{New average} = \frac{15x + 81}{16} \]

5. **Set up the equation based on the increase in average**:
- According to the problem, the new average is 3 runs more than the previous average:
\[ \frac{15x + 81}{16} = x + 3 \]

6. **Multiply both sides by 16 to eliminate the fraction**:
- This gives:
\[ 15x + 81 = 16(x + 3) \]

7. **Expand the right side**:
- Expanding gives:
\[ 15x + 81 = 16x + 48 \]

8. **Rearrange the equation to isolate \( x \)**:
- Subtract \( 15x \) from both sides:
\[ 81 = x + 48 \]
- Now, subtract 48 from both sides:
\[ x = 33 \]

9. **Calculate the average after the 16th match**:
- The new average after the 16th match is:
\[ x + 3 = 33 + 3 = 36 \]

### Final Answer:
The average after the 16th match is **36 runs**.