A cricketer has a mean score of 60 runs in 10 innings. How many runs must be scored in the 11th inning to raise the overall mean to 62?

Introduction / Context:
Average-raising problems hinge on total runs needed for the new mean over the new count. Compute the new required total, subtract the current total, and the difference is the runs needed in the next inning.

Given Data / Assumptions:

• Current mean = 60 over 10 innings.
• Target mean = 62 over 11 innings.

Concept / Approach:
Total = average * number of innings. Required 11th score = (target average * 11) − (current average * 10).

Step-by-Step Solution:

Verification / Alternative check:
After scoring 82, new total 682 / 11 = 62 exactly; condition satisfied.

Why Other Options Are Wrong:
80, 81, 83: Each yields a mean slightly below or above 62 when divided by 11.

Common Pitfalls:
Using 62 − 60 = 2 and adding 2 runs (incorrect), or dividing by 10 instead of 11 for the target total.

Final Answer:
82