A batsman scores 98 runs In the 17th match of his career. His average runs per match increased by 2.5. What is his average before the 17th match?

Options

A. 58
B. 60.5
C. 63
D. 55.5

Answer

To solve the problem, we need to find the average runs scored by the batsman before the 17th match. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Define Variables:**
Let the average runs scored by the batsman before the 17th match be \( x \).

2. **Calculate Total Runs Before the 17th Match:**
Since the batsman played 16 matches before the 17th match, the total runs scored in those 16 matches would be:
\[ \text{Total Runs} = 16x \]

3. **Add Runs Scored in the 17th Match:**
In the 17th match, the batsman scored 98 runs. Therefore, the total runs after the 17th match would be:
\[ \text{Total Runs After 17 Matches} = 16x + 98 \]

4. **Calculate New Average After 17 Matches:**
The average after 17 matches can be calculated as:
\[ \text{New Average} = \frac{16x + 98}{17} \]

5. **Set Up the Equation:**
According to the problem, the new average is 2.5 runs more than the previous average \( x \). Therefore, we can set up the equation:
\[ \frac{16x + 98}{17} = x + 2.5 \]

6. **Eliminate the Fraction:**
To eliminate the fraction, multiply both sides of the equation by 17:
\[ 16x + 98 = 17(x + 2.5) \]

7. **Distribute on the Right Side:**
Expanding the right side gives:
\[ 16x + 98 = 17x + 42.5 \]

8. **Rearrange the Equation:**
Now, let's rearrange the equation to isolate \( x \):
\[ 16x + 98 - 42.5 = 17x \]
\[ 55.5 = 17x - 16x \]
\[ 55.5 = x \]

9. **Conclusion:**
Thus, the average runs scored by the batsman before the 17th match is:
\[ \boxed{55.5} \]