A cricketer has a certain batting average for 10 innings. In the eleventh innings he scores 108 runs, thereby increasing his average by 6 runs. What is his new batting average?

Introduction / Context:
This question tests your understanding of how a single very high score can increase a batting average and how to use algebra to find both the old and the new averages.

Given Data / Assumptions:
- Before the eleventh innings, the cricketer has played 10 innings with some average A runs.
- In the eleventh innings he scores 108 runs.
- As a result, his average increases by 6 runs, becoming A + 6.
- We are asked to find the new average A + 6.

Concept / Approach:
Let the original average be A. The total runs before the eleventh innings are 10A. After scoring 108 runs, his total runs become 10A + 108 over 11 innings, and his new average is A + 6. Equating these two expressions for the new total allows us to solve for A and then compute the new average.

Step-by-Step Solution:
Step 1: Let the initial average after 10 innings be A runs. Then total runs before the 11th innings are 10A. Step 2: In the 11th innings he scores 108 runs, so new total runs = 10A + 108. Step 3: The new average is A + 6 runs over 11 innings, so new total = 11 * (A + 6). Step 4: Set the two expressions equal: 10A + 108 = 11(A + 6). Step 5: Expand the right side: 10A + 108 = 11A + 66. Step 6: Rearrange: 108 - 66 = 11A - 10A, giving 42 = A. Step 7: The new average is A + 6 = 42 + 6 = 48 runs.

Verification / Alternative check:
Check totals: with average 42 over 10 innings, total runs are 420. Adding 108 gives 528 runs over 11 innings. Then 528 / 11 = 48 runs, confirming that the new average is indeed 48.

Why Other Options Are Wrong:
- Option 44 runs: This would mean an increase of only 2 runs from a hypothetical average of 42, not 6.

- Option 46 runs: This corresponds to a smaller increase and does not fit the equation 10A + 108 = 11(A + 6).

- Option 49 runs: This would imply an average increase of 7 runs, which contradicts the given information that the increase is 6 runs.

Common Pitfalls:
A common mistake is to directly average 108 with some guessed value or to forget that the average is over 11 innings, not 10. Others mis-handle the algebra when distributing 11 over (A + 6). Writing the equation slowly and carefully helps avoid these errors.

Final Answer:
The new batting average of the cricketer is 48 runs.