A batsman scores 85 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 question uses the relationship between total runs, number of innings, and batting average in cricket. You are told how much the average increases after a particular innings, and you must work backwards to find the new average.

Given Data / Assumptions:
Number of innings before the latest one = 16. Runs scored in the 17th innings = 85. The batting average increases by 3 runs due to this innings. Let the old average (before the 17th innings) be A runs. New average after 17 innings = A + 3.

Concept / Approach:
Average runs per innings = Total runs / Number of innings. If the old average is A, then: Total runs in 16 innings = 16 * A. After scoring 85 runs in the 17th innings: New total runs = 16A + 85. The new average is (16A + 85) / 17, which is given to be A + 3. This leads to an equation in A that we can solve.

Step-by-Step Solution:
Step 1: Set up the equation for the new average. (16A + 85) / 17 = A + 3. Step 2: Cross multiply to eliminate the denominator. 16A + 85 = 17(A + 3). Step 3: Expand the right-hand side. 16A + 85 = 17A + 51. Step 4: Rearrange to solve for A. 85 - 51 = 17A - 16A. 34 = A. So, the old average is 34 runs. Step 5: New average = A + 3 = 34 + 3 = 37.

Verification / Alternative Check:
If the average before the 17th innings is 34, total runs in 16 innings = 16 * 34 = 544. After scoring 85 runs, total runs = 544 + 85 = 629. New average = 629 / 17 = 37, confirming the calculation.

Why Other Options Are Wrong:
34: This is the old average, not the new one. 35 and 36: These do not correspond to a 3-run increase from any integer average that fits the given score of 85. 38: This would require a larger increase than 3 runs from the previous average.

Common Pitfalls:
Some students mistakenly assume that 85 is simply 3 more than the old average times the new number of innings, without setting up the correct equation. Others forget to multiply the new average by 17 innings when relating it to the total runs. Always start from the definition of average and write a clear equation.

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