A batsman scores 95 runs in his 13th match and thereby increases his average runs per match by 4. What is his average after the 13th match?

Introduction:
Batting average equals total runs divided by matches played. Here, scoring 95 in the 13th match raises the average by 4. We set up an equation with the old and new averages using totals before and after the match.

Given Data / Assumptions:
Matches before latest = 12. Runs in 13th match = 95. Increase in average after 13th = 4. Let old average be A; new average = A + 4.

Concept / Approach:
Total runs before = 12 * A. After the 13th match, total runs = 12A + 95 over 13 matches. So (12A + 95) / 13 = A + 4. Solve for A, then compute A + 4.

Step-by-Step Solution:
(12A + 95) / 13 = A + 4. 12A + 95 = 13A + 52. 95 − 52 = 13A − 12A ⇒ A = 43. New average = A + 4 = 43 + 4 = 47.

Verification / Alternative check:
Total runs before = 12 * 43 = 516. After scoring 95, total = 611. New average = 611 / 13 = 47, confirming the result.

Why Other Options Are Wrong:
43: This is the old average, not the new one. 45, 46, 49: Do not match the increase of 4 when combined with a feasible old average given a 95-run innings.

Common Pitfalls:
Averaging 95 with the old average directly or forgetting to divide the new total by 13. Always write the equation using totals and solve systematically.

Final Answer:
The new batting average is 47 runs per match.