A batsman scores 98 runs in the 17th match of his career. As a result, his average runs per match increase by 2.5 runs. What was his batting average per match before playing the 17th match?

Introduction / Context:
This is another cricket averages question. The batsman has a certain average over his first 16 matches. After scoring 98 runs in the 17th match, his overall average increases by 2.5 runs per match. We are asked to find his original average before the 17th match. This type of question tests your ability to convert average information into equations and solve for unknowns.

Given Data / Assumptions:
- Number of matches before the latest match = 16.
- Let the old average be a runs per match.
- In the 17th match, the batsman scores 98 runs.
- New average after 17 matches is a + 2.5 runs per match.
- We need to find the old average a.

Concept / Approach:
The total runs before the 17th match can be written as 16a. After the 17th match, the total runs become 16a + 98. The new average is this total divided by 17, and the problem tells us that this value is a + 2.5. Using this fact, we create an equation involving a and solve it. The process is very similar to other average change problems and relies on careful algebra.

Step-by-Step Solution:
Step 1: Old total runs in 16 matches = 16a.Step 2: After scoring 98 in the 17th match, new total runs = 16a + 98.Step 3: New average after 17 matches = (16a + 98) / 17.Step 4: We are told this equals a + 2.5, so (16a + 98) / 17 = a + 2.5.Step 5: Multiply both sides by 17: 16a + 98 = 17a + 42.5.Step 6: Rearrange: 16a + 98 - 17a - 42.5 = 0, giving -a + 55.5 = 0.Step 7: Hence a = 55.5.Step 8: Therefore, the batsman average before the 17th match was 55.5 runs per match.

Verification / Alternative check:
If a = 55.5, then total runs after 16 matches are 16 * 55.5 = 888 runs. Adding 98 from the 17th match gives new total runs of 986. New average after 17 matches is 986 / 17 = 58 runs per match. The increase in average is 58 - 55.5 = 2.5 runs, which matches the condition given. This confirms that the original average of 55.5 runs is correct.

Why Other Options Are Wrong:
If the old average had been 58, 60.5, 63 or 57, then using the same process would not produce an increase of exactly 2.5 runs after scoring 98. For instance, if a were 58, the new total after 17 matches would give a different new average increment than 2.5. Only a value of 55.5 satisfies the equation built from the given conditions.

Common Pitfalls:
Sometimes students mistakenly divide by 16 instead of 17 when computing the new average, or they set the new average equal to 2.5 rather than a + 2.5. Carefully label the old average, old total, new total and new average, and double check that the number of matches in the denominator matches the number of matches played at that stage.

Final Answer:
The batsman average before the 17th match was 55.5 runs per match.