The average score of 120 students in a test is 70. If the average score of the passed students is 78 and that of the failed students is 30, then what is the number of failed students?

Correct option is A

Given:

Average marks of 120 students = 70.
Average marks of passed students = 78.
Average marks of failed students = 30
Formula Used:
Total marks = number of students * average marks
Solution:
=> Total marks of 120 students = 120 * 70 = 8400.
=> Let the number of students who passed be x.
=> Total marks of passed students + total marks of failed students = Total marks of all students.
=> 78x + 30(120-x) = 8400.
=> 48x = 4800.
=> x = 4800 / 48 = 100.

Number of failed students is 120-100 = 20 students

Alternate Method:

​$$\begin{array}{c}\quad \quad \text{Avg. Score of passed students} \quad \quad \quad \text{Avg. Score of failed students} \\\quad \quad 78 \quad \quad \quad \quad \quad 30 \\\quad \quad \diagdown \quad \quad \quad \quad \diagup\\ \quad \quad \quad \quad \quad 70 \quad \quad \quad \\\quad \quad \diagup \quad \quad \quad \quad \diagdown\\\quad \quad 40 \quad \quad \quad \quad \quad 8 \\\quad \quad \text{Number of passed students} \quad \quad \quad \text{Number of failed students} \\\end{array}$$

So, Total Students are 120 

then Number of Failed Students = $$\frac{8}{48}\times 120 = 20$$​​