A batsman scores 85 runs in his 17th innings, and as a result his batting average increases by 3 runs. What is his batting average after completing the 17th innings?

Introduction / Context:
Batting average questions are standard applications of average formulas. The important idea is that when a new score is added, the new average depends on both the old average and the new score. This question asks you to determine the new average from the information that a single innings increased the average by a known amount.

Given Data / Assumptions:

• Before the 17th innings, the batsman has played 16 innings.

• His average before the 17th innings is some value A (in runs per innings).

• In the 17th innings, he scores 85 runs.

• After this innings, his average increases by 3 runs, so new average = A + 3.

• We need to find the new average after 17 innings.

Concept / Approach:
Let A be the old average. Then the total runs scored in the first 16 innings is 16 * A. After scoring 85 in the 17th innings, his new total runs are 16 * A + 85. His new average after 17 innings is given as A + 3, so we set up the equation (16A + 85) / 17 = A + 3 and solve for A. Once A is known, we add 3 to obtain the new average after 17 innings.

Step-by-Step Solution:
Let old average = A runs per innings. Total runs in 16 innings = 16 * A. Runs in 17th innings = 85. Total runs after 17 innings = 16A + 85. New average after 17 innings = A + 3. So, (16A + 85) / 17 = A + 3. Multiply both sides by 17: 16A + 85 = 17A + 51. Rearrange: 85 − 51 = 17A − 16A, so 34 = A. Old average A = 34, therefore new average = A + 3 = 37.

Verification / Alternative check:
Using A = 34, total runs before 17th innings = 16 * 34 = 544. Adding the 17th innings score: 544 + 85 = 629 runs. New average = 629 / 17. Since 17 * 37 = 629, the new average is exactly 37 runs per innings. This confirms that the calculations are consistent and the answer is correct.

Why Other Options Are Wrong:
A new average of 34, 35 or 36 would imply a smaller increase than the stated 3 runs, given a score of 85. Substituting any of those values into the equation would give inconsistent values of the old average or total runs. Only 37 satisfies both the increase of 3 runs and the specific additional score of 85 runs in the 17th innings.

Common Pitfalls:
A common mistake is to assume the given increase applies directly to the total runs instead of the average, or to misapply the formula total = average * number of innings. Some students also forget to divide total runs by the new number of innings, which is 17, not 16. Setting up the equation carefully and checking each step helps prevent these errors.

Final Answer:
The batsman's batting average after the 17th innings is 37 runs per innings.