The average marks of a class of 60 students is 65. The average marks of half of the students (30 students) is 85. What is the average marks of the remaining 30 students?

Introduction:
Overall average with subgroup average known lets you find the complement subgroup average by using totals. Compute totals from averages and subtract to find the remaining group's sum and average.

Given Data / Assumptions:
Total students = 60, class average = 65 ⇒ total marks = 60 * 65 = 3900. Top half (30 students) average = 85 ⇒ their total = 30 * 85 = 2550. Remaining half = 30 students.

Concept / Approach:
Remaining group total = overall total − known group total. Divide by 30 to get the remaining group's average.

Step-by-Step Solution:
Remaining total = 3900 − 2550 = 1350. Remaining average = 1350 / 30 = 45.

Verification / Alternative check:
Weighted average check: (30 * 85 + 30 * 45) / 60 = (2550 + 1350)/60 = 3900/60 = 65, consistent with the class average.

Why Other Options Are Wrong:
35, 55, 65, 40: None match the exact complementary average computed from totals.

Common Pitfalls:
Averaging 85 and 65 directly or making assumptions about distribution. The complement must satisfy the total-marks constraint.

Final Answer:
The average of the remaining students is 45.