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

Introduction:
Bowling average = total runs conceded / total wickets. When a final performance is appended, the updated average can be written in terms of the previous totals plus the last match’s figures. Solving the resulting equation gives the number of wickets before the last match (as asked).

Given Data / Assumptions:

• Old average = 12.4 runs/wicket.
• Last-match performance: 26 runs for 5 wickets.
• New average = 12.4 − 0.4 = 12.0 runs/wicket.
• Question explicitly asks for wickets before the last match.

Concept / Approach:
Let old wickets = x, so old runs = 12.4x. After the last match: wickets = x + 5, runs = 12.4x + 26. Set (12.4x + 26) / (x + 5) = 12 and solve for x.

Step-by-Step Solution:

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

Why Other Options Are Wrong:
75, 79, 81, and 72 do not satisfy the average equation when substituted back.

Common Pitfalls:
Reporting the total wickets after the match (90) when the question asks for the count before the last match.

Final Answer:
85