In a college union, there are 48 students. The ratio of the number of boys to the number of girls is 5 : 3. The number of girls to be added in the union, so that the number of boys to girls in 6 : 5 is = ?

And ratio of numbers of boys to the number of girls is 5x : 3x
According to the question,
$$\eqalign{ & \Rightarrow 5x + 3x = 48 \cr & \Rightarrow 8x = 48 \cr & \Rightarrow \boxed{x = 6} \cr & {\text{Boys}} = 30 \cr & {\text{Girl}} = 18 \cr & {\text{Now,}}\frac{{30}}{{18 + y}} = \frac{6}{5} \cr & \Rightarrow 25 = 18 + y \cr & \Rightarrow y = 7 \cr} $$