The average marks of a group of 16 students in a test are reduced by 4 when the topper, who scored 92 marks, is replaced by a new student. What are the marks scored by the new student?

Let's assume the initial average mark of 16 students is 'y'.

Total marks of 16 students initially = 16y    Eq.(i)

The average marks of a group of 16 students in a test are reduced by 4 when the topper, who scored 92 marks, is replaced by a new student.

now the average marks of a group of 16 students = (y-4)

Total marks of 16 students now = 16(y-4)    Eq.(ii)

Let's assume the mark of the new student is 'z'.

Eq.(i) - 92 = Eq.(ii) - z

16y - 92 = 16(y-4) - z

16y - 92 = 16y - 64 - z

-92 = -64 - z

z = 92-64

Marks scored by the new student = z = 28