A batsman scores 87 runs in his 17th innings and thereby increases his batting average by 3 runs. What is his batting average after the 17th innings?

Introduction:
This averages question comes from cricket statistics. When a batsman plays one more innings, his average can change depending on the new score. You are told his 17th innings score and how much his average increases, and must deduce his new average. This type of problem tests understanding of how totals and averages are related.

Given Data / Assumptions:

• Before the 17th innings, he had completed 16 innings.
• Let his previous average be A runs per innings.
• In the 17th innings, he scores 87 runs.
• After this innings, his average increases by 3 runs, so his new average is A + 3.
• We are asked to find the new average after 17 innings.

Concept / Approach:
Average = (total runs) / (number of innings). Let the total runs before the 17th innings be 16A. After scoring 87 runs in the 17th innings, his new total runs become 16A + 87, and his new average over 17 innings is (16A + 87)/17. This new average is given to be A + 3. Equating these expressions leads to a linear equation in A.

Step-by-Step Solution:
Let previous average be A runs.Total runs after 16 innings = 16A.In the 17th innings he scores 87, so new total = 16A + 87.New average after 17 innings = (16A + 87) / 17.Given that this new average is 3 runs more than A, we have:(16A + 87) / 17 = A + 3.Multiply both sides by 17:16A + 87 = 17A + 51.Rearrange:87 − 51 = 17A − 16A ⇒ 36 = A.So previous average A = 36 runs.New average = A + 3 = 36 + 3 = 39 runs.

Verification / Alternative check:
Check with actual totals. If average after 16 innings is 36, then total runs = 16 * 36 = 576. Adding 87 gives new total = 663. Divide by 17: 663 / 17 = 39, which is indeed 3 runs more than 36. This confirms that the new average is 39 runs.

Why Other Options Are Wrong:
40, 50 and 55 are too high and do not satisfy the equation (16A + 87)/17 = A + 3 for any integer previous average. The value 36 is the old average, not the new one, so it does not answer the question. Only 39 is consistent with all the given information.

Common Pitfalls:
Some students confuse the old and new averages and mistakenly report A instead of A + 3. Others may incorrectly set up the equation, such as writing 16A + 87 = 17(A + 3) incorrectly or forgetting to multiply the new average by the number of innings. Careful mapping of total runs before and after the new innings is crucial.

Final Answer:
The batsman's average after the 17th innings is 39 runs per innings.