A bowler’s average is 12.4 runs per wicket. In his last match he took 5 wickets for 26 runs and his overall bowling average decreased by 0.4. How many wickets had he taken before his last match?

Introduction: Bowling average = total runs conceded / total wickets. When a new performance is added, the updated average can be expressed in terms of the prior totals plus the last match’s runs and wickets. This yields a linear equation in the unknown prior wickets.

Given Data / Assumptions:

• Prior average = 12.4 runs/wicket
• Last match: 5 wickets for 26 runs
• New average = 12.4 − 0.4 = 12.0 runs/wicket

Concept / Approach: Let prior wickets = x and prior runs = 12.4x. After the last match: wickets = x + 5; runs = 12.4x + 26. Set new average = (12.4x + 26) / (x + 5) = 12 and solve for x.

Step-by-Step Solution:

Verification / Alternative check: New totals: runs = 12.4 * 85 + 26 = 1054 + 26 = 1080; wickets = 85 + 5 = 90; 1080 / 90 = 12.0, confirming the drop by 0.4.

Why Other Options Are Wrong: 78, 72, and 64 do not satisfy the equation; 90 would give an average different from 12.0 after adding the last match’s performance.

Common Pitfalls: Averaging averages or mixing up the order of addition; always work with total runs and total wickets.

Final Answer: 85