Batting average drop after a high score: A batsman has a certain average for 11 innings. In the 12th innings he scores 90 runs and his average decreases by 5. What is his average after 12 innings?

Introduction / Context:
Averages in cricket can move in nonintuitive ways. Setting up an equation for totals before and after the nth innings resolves the value.

Given Data / Assumptions:

• Average after 11 innings = A
• Score in 12th = 90
• Average after 12 innings = A - 5

Concept / Approach:
Relate totals: 11*A + 90 = 12*(A - 5). Solve for A, then compute A - 5.

Step-by-Step Solution:

Verification / Alternative check:
Total after 11 = 1650. After 12 with score 90 total = 1740. 1740/12 = 145. Works.

Why Other Options Are Wrong:

• 127, 150, 217: Do not match the derived post 12th average.

Common Pitfalls:
Forgetting the average decreases despite a high single score due to a very high prior average.

Final Answer: