The average marks obtained by a group of 45 students were 16.2. One student left the group as a result of which the average of the remaining students rose to 16.5. But another student came in as a result of which the average marks of the group dropped a bit and became 16.4. What were the average marks obtained by the student who left and the one who joined?

Correct option is D

​Given:
​Number of students initially = 45

Initial average marks = 16.2

After one student left, new average = 16.5

After another student joined, final average = 16.4

Formula Used:

Total marks = Number of students × Average marks

Marks of the student who left = Initial total marks - New total marks after the student left

Marks of the student who joined = Final total marks - Total marks after the student left

Solution:

Initial total marks = 45 × 16.2 = 729​

After one student left, total students = 44

New total marks after one student left = 44 × 16.5 = 726

Marks of the student who left = 729 - 726 = 3

Another student add=45$$\times$$16.4=738

Now, 738 -726= 12

Average marks obtained by the student who left and the one who joined=$$\frac{12+ 3}{2}= \frac{15}{2}=7.5$$​