In a class, there are 80 students and their average marks in the annual examination are 40. If the average marks of passed students are 60 and average marks of failed students are 35, then find out the number of students who failed.

Let the number of failed student = Y
∴ Number of passed student = 80 - Y
sum of marks of all students = sum of marks of passed students + sum of marks of failed students
80 x 40 = (80 - Y) x 60 + 35Y
⇒ 3200 =4800 - 60Y + 35Y
⇒ 25Y = 1600
∴ Y = 64
∴ Number of students who failed = 64