Cricket batting average adjustment: A batsman has a certain average for 14 innings. In the 15th innings he scores 72 runs, and his average increases by 2 runs. What is his new average after 15 innings?

Introduction / Context:This problem tests average (arithmetic mean) update when one additional data point is appended and the average changes by a known amount.

Given Data / Assumptions:

• Average after 14 innings = x
• 15th score = 72
• New average increases by 2, so new average = x + 2

Concept / Approach:For n items with average x, total is n * x. After adding a new score s, new average is (n * x + s) / (n + 1). Set this equal to x + 2 and solve for x, then compute the new average.

Step-by-Step Solution:(14 * x + 72) / 15 = x + 214x + 72 = 15x + 3072 - 30 = 15x - 14xx = 42New average = x + 2 = 44

Verification / Alternative check:Total after 14 innings = 14 * 42 = 588. Add 72 gives 660. 660 / 15 = 44. Correct.

Why Other Options Are Wrong:46, 42, 48, 40 are inconsistent with the equation and totals computed above.

Common Pitfalls:Confusing the previous average with the new one or dividing by 14 instead of 15 after the last innings.

Final Answer:44