Given, Average marks of 240 students = 37
Average marks of failed students = 17
Average marks of passed students = 41
Formula: Average = Sum of all observations / total number of all observations
Calculation: Let number of failed students be x, then
Number of passed students = 240 - x
According to the question
x×17+(240−x)×41=240×37 ⇒
17x+9840−41x=8880 ⇒
41x−17x=9840−8880 ⇒
24x=960⇒x= ⇒
x=40 ∴ Number of failed students is 40.
Alternate Method
20Hence, failed students : passed students = 4 : 20 = 1 : 5∴ Failed students = Total students × (1/6) = 240/6 = 40