A batsman scores 98 runs in the 17th match of his career, and as a result his average runs per match increases by 2.5 runs. What was his average runs per match before playing this 17th match?

Introduction / Context:
This problem tests the concept of average in the context of cricket statistics. We are given the score in a particular match and the change in the overall average after that match. From this, we need to work backwards to find the original average runs per match before the latest innings. Such questions are common in aptitude exams and help in understanding how averages behave when a new value is added.

Given Data / Assumptions:

• Total matches before the latest innings = 16
• Runs scored in the 17th match = 98
• Increase in average after the 17th match = 2.5 runs
• Let the old average before the 17th match be a runs per match

Concept / Approach:
The key idea is that: average = total runs / number of matches. Before the 17th match, the batsman has 16a total runs. After scoring 98 runs in the 17th match, his total runs become 16a + 98 and the number of matches becomes 17. We are told that the new average is 2.5 runs more than the old average, so we can form an equation involving a and solve it.

Step-by-Step Solution:
Let the old average = a runs per match. Total runs before 17th match = 16 * a. After 17th match, total runs = 16 * a + 98. Number of matches after 17th match = 17. New average = (16 * a + 98) / 17. Given that new average = old average + 2.5, so: (16 * a + 98) / 17 = a + 2.5. Multiply both sides by 17: 16 * a + 98 = 17 * a + 42.5. Rearrange: 98 - 42.5 = 17 * a - 16 * a. 55.5 = a. Therefore, the old average = 55.5 runs per match.
Verification / Alternative check:
Total runs before 17th match = 16 * 55.5 = 888 runs. After scoring 98 runs, total = 888 + 98 = 986 runs. New average = 986 / 17 = 58 runs per match. Increase in average = 58 - 55.5 = 2.5 runs, which matches the given condition.
Why Other Options Are Wrong:
Option A (58): This is actually the new average after the 17th match, not the old one. Option B (60.5): Gives a different increase in average and does not satisfy the equation. Option C (63): Also fails when substituted, leading to an incorrect new average. Option D (55.5): Correct, as it satisfies all the given conditions.
Common Pitfalls:
A common mistake is to directly average 98 with some guessed old average instead of using the total runs approach. Another error is to assume that the increase in average is equal to the difference between 98 and the old average, which is not true because the average involves many matches. Students sometimes miscount the number of matches before and after the innings, leading to a wrong equation.
Final Answer:
The batsman's average runs per match before the 17th match was 55.5 runs.