A batsman is playing his twelfth innings. After scoring 26 runs in this innings, his batting average increases from 14 to 15 runs per innings. How many runs must he score in total in this same innings so that his average becomes 19 runs per innings?

Introduction / Context:
This question checks your understanding of averages in the context of cricket scores. The key ideas are how an additional innings affects the batting average and how to use the formula for average to move from the old average to a new target average within the same innings.

Given Data / Assumptions:
- Before the current innings, the batsman has completed 11 innings with an average of 14 runs.
- While playing his twelfth innings, after scoring 26 runs, his average becomes 15 runs per innings.
- We assume 26 is the partial score so far in this twelfth innings when the average first reaches 15.
- We need the total score in this same twelfth innings that will raise his average to 19 runs per innings.

Concept / Approach:
Batting average is defined as total runs scored divided by number of innings played. First, we use the given information about the average changing from 14 to 15 to find how many innings he has already completed. Then we use the required final average of 19 over the same number of innings (still 12) to find the total runs needed in this innings, which directly gives the required total score, not just extra runs beyond 26.

Step-by-Step Solution:
Step 1: Let the number of innings before this match be n. His total runs before this innings are 14 * n. Step 2: After scoring 26 runs in this twelfth innings, the new average becomes 15, so (14 * n + 26) / (n + 1) = 15. Step 3: Solving 14n + 26 = 15n + 15 gives n = 11, so this is his twelfth innings. Step 4: Total runs after 12 innings for an average of 15 are 15 * 12 = 180. Step 5: To have an average of 19 over 12 innings, his total runs must be 19 * 12 = 228. Step 6: Therefore, his total score in this twelfth innings must be 228 - (total runs before this innings), that is 228 - 14 * 11 = 228 - 154 = 74.

Verification / Alternative check:
If he scores 74 runs in the twelfth innings, his total runs become 154 + 74 = 228. The new average is 228 / 12 = 19 runs per innings, exactly as required. Thus, the answer is consistent.

Why Other Options Are Wrong:
- Option 79: With 79 runs, total runs are 154 + 79 = 233, giving an average of 233 / 12 which is greater than 19.
- Option 72: With 72 runs, total runs are 154 + 72 = 226, giving an average below 19.
- Option 60: With 60 runs, the total is 214, and the average is much less than 19.

Common Pitfalls:
A common error is to treat 26 as the final score in the innings instead of a partial score at which the average first becomes 15. Another mistake is to try to first calculate an intermediate average and then guess extra runs. The safest approach is always to write clear equations for total runs before and after the innings and use the definition of average systematically.

Final Answer:
The batsman must score a total of 74 runs in this twelfth innings to raise his average to 19.