Delhi Police Constable Exam Model Paper 4

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
$\mathit{x}\times 17+\left(240-\mathit{x}\right)\times 41=240\times 37$
⇒ $17\mathit{x}+9840-41\mathit{x}=8880$
⇒ $41\mathit{x}-17\mathit{x}=9840-8880$
⇒ $24\mathit{x}=960\Rightarrow \mathit{x}=\frac{960}{24}$
⇒ $\mathit{x}=40$
∴ 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