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?

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