The average marks obtained by a class in an examination were calculated as 30.5. However, while checking the marks enter...

Question

The average marks obtained by a class in an examination were calculated as 30.5. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 42 instead of 24. After correcting the marks, the average becomes 30. How many students does the class have?

A. 29
B. 28
C. 36
D. 32

Accepted Answer

The class has 36 students. The average changed because one student's marks were over-counted by 42 - 24 = 18. This excess 18 spread across all n students caused the average to drop by 30.5 - 30 = 0.5. Dividing the total excess by the drop in average gives the number of students: 18 / 0.5 = 36.