Explanation: To solve this problem, we need to understand the relationship between the total runs scored, the number of matches played, and the average score. The average score is calculated by dividing the total runs by the number of matches. Let's denote the initial average before the 17th match as \( A \).
Given:
- The batsman scores 87 runs in the 17th match.
- The average increases by 3 after the 17th match.
Let's denote the total runs scored in the first 16 matches as \( R \). The average before the 17th match is given by:
\[ A = \frac{R}{16} \]
After the 17th match, the total runs scored become \( R + 87 \), and the number of matches becomes 17. The new average is:
\[ A + 3 = \frac{R + 87}{17} \]
We can substitute \( R \) from the first equation into the second equation:
\[ A + 3 = \frac{16A + 87}{17} \]
To solve for \( A \), we first eliminate the fraction by multiplying both sides by 17:
\[ 17(A + 3) = 16A + 87 \]
Expanding and simplifying:
\[ 17A + 51 = 16A + 87 \]
\[ 17A - 16A = 87 - 51 \]
\[ A = 36 \]
Thus, the initial average before the 17th match is 36. This matches the correct answer provided.
The key to solving this problem is understanding how the average changes with the addition of a new score and using algebra to set up and solve the equation. The concept of average and its relationship to total runs and number of matches is crucial in solving such problems.