Sripad has an average score of 65 marks in three subjects. In no subject has he scored less than 58 marks, and he has scored strictly more marks in Mathematics than in each of the other two subjects. What is the maximum possible score he could have obtained in Mathematics?

Introduction / Context:
This is an average-based reasoning question combined with inequality constraints. Sripad's average in three subjects is given, and there are lower bounds on his marks in each subject, plus the condition that his Mathematics score is strictly higher than his other two scores. We must find the maximum possible score he could have in Mathematics while respecting all constraints.

Given Data / Assumptions:

• Number of subjects = 3.
• Average marks across the three subjects = 65.
• Therefore, total marks in all 3 subjects = 3 * 65 = 195.
• In each subject he scored at least 58 marks.
• Mathematics score is strictly greater than the scores in the other two subjects.
• We seek the maximum possible value of the Mathematics score.

Concept / Approach:
To maximize the Mathematics score, we should minimize the other two subject scores, subject to the given constraints. Since each of the other two subjects must be at least 58 and less than Maths, the smallest possible allowed marks for them is 58 each. Once we assign these minima, we can compute the remaining marks available for Mathematics by subtracting from the total of 195.

Step-by-Step Solution:
Step 1: Let the three subjects be Maths (M), Subject 2 (S2), and Subject 3 (S3). Step 2: Total marks M + S2 + S3 = 195. Step 3: Constraints: S2 ≥ 58, S3 ≥ 58, and M > S2, M > S3. Step 4: To maximize M, minimize S2 and S3 while respecting S2 ≥ 58 and S3 ≥ 58. So set S2 = 58 and S3 = 58. Step 5: Compute M. M = 195 − (S2 + S3) = 195 − (58 + 58) = 195 − 116 = 79. Step 6: Check the inequality condition. M = 79, S2 = 58, S3 = 58, so Maths is greater than both other subjects, satisfying the conditions.
Verification / Alternative check:
If we try to increase M beyond 79, the total 195 would force the sum of S2 and S3 to drop below 116, making at least one of them less than 58, which is not allowed. For example, if M were 80, then S2 + S3 = 195 − 80 = 115, so the average of S2 and S3 would be 57.5, meaning one of them is at most 57, violating the minimum 58 constraint.
Why Other Options Are Wrong:
Options B (77), C (76), D (73) and E (72) are all possible scores for Maths that satisfy the constraints, but they are not the maximum possible value. The question asks for the maximum score, which is achieved precisely at 79.
Common Pitfalls:
A common mistake is to ignore the 'no subject less than 58' condition and assume that the other scores can be much smaller, leading to an incorrect higher Maths score. Another error is to forget the strict inequality that Maths must be greater than the other two subjects, not just equal.
Final Answer:
The maximum possible score Sripad could have obtained in Mathematics is 79.