Sripad scores an average of 65 marks in three subjects. In no subject does he score less than 58 marks, and he scores more marks in Mathematics than in the other two subjects. What is the maximum possible score he could obtain in Mathematics?

Introduction / Context:
This question is about averages and constraints. You are given a fixed average over three subjects and lower bounds on each subject, and you must find how large one particular subject score can be while respecting all conditions.

Given Data / Assumptions:
- There are three subjects in total, including Mathematics.
- The average of the three subject scores is 65 marks, so the total is fixed.
- In every subject, the score is at least 58 marks.
- The Mathematics score is higher than the scores in the other two subjects.
- We need the maximum possible score in Mathematics.

Concept / Approach:
Since the average is fixed, the sum of the three scores is fixed. To maximise one subject, we minimise the other two while respecting their minimum allowed values. Once we fix the two smaller scores at their minimum values, the remaining marks go to Mathematics, which yields the maximum possible Mathematics score.

Step-by-Step Solution:
Step 1: Let the three subject scores be M (Maths), S1 and S2. Step 2: Average = 65, so M + S1 + S2 = 3 * 65 = 195. Step 3: Each subject must have at least 58 marks, and Mathematics must be greater than both S1 and S2. Step 4: To maximise M, choose S1 = 58 and S2 = 58, the smallest values allowed. Step 5: Then M = 195 - 58 - 58 = 195 - 116 = 79. Step 6: This value 79 is greater than 58, so the condition that Maths has the highest score is satisfied.

Verification / Alternative check:
If you try to increase either S1 or S2 above 58, the total 195 forces M to become smaller. Therefore, choosing both non Maths subjects at their minimum gives the largest possible M. No value greater than 79 is possible because that would make the sum exceed 195.

Why Other Options Are Wrong:
- Option 77: If M = 77 and S1, S2 are at least 58, then total is at least 77 + 58 + 58 = 193, which is less than 195, meaning the average would not be 65.

- Option 76: Similar reasoning gives a total less than 195 with minimum other scores, or would require one subject under 58.

- Option 73: This is a possible Maths score but not the maximum; we have already shown 79 is possible under the constraints.

Common Pitfalls:
Students sometimes forget to consider the minimum bound of 58 for each subject and instead assume the other subjects can go arbitrarily low. Another issue is trying to distribute marks evenly, which contradicts the condition that Maths has the highest score. Always use the idea that to maximise one quantity under a sum constraint, you minimise the others within their allowed ranges.

Final Answer:
The maximum possible score in Mathematics is 79 marks.