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?
Aptitude
Average
Difficulty: Medium
Choose an option
Answer
Correct Answer: 145
Explanation
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:
11*A + 90 = 12*A - 6090 + 60 = 12*A - 11*A150 = AAverage after 12 = A - 5 = 145Verification / 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:
145