An expenditure of Rs. 96 was supposed to be shared equally by all the students in a class. Since four students didn't contribute, the remaining students had to contribute an additional amount of Rs. 4, each. How many students contributed?

Correct option is A

Given:
Total expenditure = Rs. 96
Each student was supposed to contribute equally
4 students didn’t contribute
The remaining students paid Rs. 4 more each
We need to find the number of students who actually contributed

Solution:

$$\begin{aligned}&\text{Let total number of students be } x \\&\text{Original share per student} = \frac{96}{x} \\&\text{Number of students who actually contributed} = x - 4 \\&\text{New share per student} = \frac{96}{x - 4} \\\\&\text{Given: New share is Rs. 4 more than the original} \\&\Rightarrow \frac{96}{x - 4} - \frac{96}{x} = 4 \\\\&\text{Multiply both sides by } x(x - 4): \\&96x - 96(x - 4) = 4x(x - 4) \\&96x - 96x + 384 = 4x^2 - 16x \\&384 = 4x^2 - 16x \\\\&\text{Divide both sides by 4:} \\&96 = x^2 - 4x \\&x^2 - 4x - 96 = 0 \\\\&\text{Solve using quadratic formula:} \\&x = \frac{4 \pm \sqrt{(-4)^2 + 4 \cdot 1 \cdot 96}}{2 \cdot 1} \\&= \frac{4 \pm \sqrt{16 + 384}}{2} \\&= \frac{4 \pm \sqrt{400}}{2} \\&= \frac{4 \pm 20}{2} \\\\&x = \frac{24}{2} = 12 \quad \text{(valid)}, \quad x = \frac{-16}{2} = -8 \quad \text{(not valid)} \\\\&\text{So, total students} = 12 \\&\text{Students who contributed} = 12 - 4 = \boxed{8}\end{aligned}$$​