In an exam the average marks for the class was 60, the average of marks of the students who passed was 70 and those failed was 30. What is the percentage of the students of the class who failed?

Correct option is A

Given:
Average marks of class = 60
Average marks of passed students = 70
Average marks of failed students = 30

Formula:
​$$\text{Overall Average} = \frac{(\text{Pass Average} \times \% \text{Pass}) + (\text{Fail Average} \times \% \text{Fail})}{100}$$​​

Solution:

Let the percentage of students who passed = p
Then, percentage of students who failed = (100 - p)

According to the formula:
60 = (70 × p + 30 × (100 - p)) ÷ 100

Multiply both sides by 100:
6000 = 70p + 3000 - 30p

Simplify:
6000 = 40p + 3000
6000 - 3000 = 40p
3000 = 40p
p = 75

Thus, percentage of students who passed = 75
Percentage of students who failed = 100 - 75 = 25

Final Answer: (a) 25