In a college the students in Arts and commerce faculties were in the ratio of 4 : 5 respectively. When 65 more students joined commerce faculty the ratio becomes 8 : 11 respectively. How many students are there in Arts faculty?

Answer: Option A

Let the number of students in Arts and Commerce faculties be 4x and 5x respectively.
Then,
$$\begin{array}{rl}& =\frac{4x}{5x+65}=\frac{8}{11}\\ & \Rightarrow 44x=8\left(5x+65\right)\\ & \Rightarrow 4x=520\\ & \Rightarrow x=130\end{array}$$
∴ Number of students in Arts faculty
= (4 × 130)
= 520