A cricketer has a certain batting average for 10 innings. In the 11th innings he scores 216 runs and his average increases by 12 runs. What is his new batting average (after 11 innings)?

Introduction: Average problems in cricket are classic applications of “total = average * count”. When a new innings is added, the new average depends on the old total plus the new score. We convert the statements into equations and solve directly.

Given Data / Assumptions:

• Let old average after 10 innings be x runs.
• 11th-innings score = 216 runs.
• New average increases by 12 → new average = x + 12.

Concept / Approach: Use totals: old total = 10x. New total = 10x + 216. New average = (10x + 216) / 11 = x + 12. Solve for x, then compute new average x + 12.

Step-by-Step Solution:

Verification / Alternative check: Old total = 10 * 84 = 840. New total = 840 + 216 = 1056. New average = 1056 / 11 = 96, which matches.

Why Other Options Are Wrong: 87 and 92 understate the increase; 97 overstates; 84 is the old average, not the new one.

Common Pitfalls: Averaging the two numbers 84 and 216 (which is meaningless here) or dividing 216 by 11 directly. Always work via totals.

Final Answer: 96