The average marks obtained by a class of 60 students is 65. The average marks of half of the students is found to be 85. The average marks of the remaining students is

Options

A. 35
B. 45
C. 55
D. 65

Answer

To solve the problem step by step, we will follow these calculations:

1. **Understand the Given Information**:
- Total number of students = 60
- Average marks of all students = 65
- Average marks of half the students (30 students) = 85

2. **Calculate the Total Marks for All Students**:
- Total marks for all students = Average marks × Total number of students
- Total marks = 65 × 60 = 3900

3. **Calculate the Total Marks for the First Group**:
- Total marks for the first group (30 students) = Average marks of the first group × Number of students in the first group
- Total marks for the first group = 85 × 30 = 2550

4. **Calculate the Total Marks for the Second Group**:
- Total marks for the second group = Total marks for all students - Total marks for the first group
- Total marks for the second group = 3900 - 2550 = 1350

5. **Calculate the Average Marks for the Second Group**:
- Average marks for the second group = Total marks for the second group / Number of students in the second group
- Average marks for the second group = 1350 / 30 = 45

Thus, the average marks of the remaining students in the second group is **45**.