The product of two positive numbers is 11520 and ir quotient is $$\frac{9}{5}$$. Find difference between two numbers.

Let x and y are two numbers (x > y)
According to the question,
$$\eqalign{ & xy = {\text{ }}11520 \cr & \frac{x}{y} = \frac{9}{5} \Rightarrow \boxed{x = \frac{{9y}}{5}} \cr & {\text{put the value of x in eq}}{\text{. (i)}} \cr & \frac{{9{\text{y}}}}{5} \times {\text{y = 11520 }} \cr & \Rightarrow {\text{ }}{{\text{y}}^2} = 6400 \cr & \Rightarrow \boxed{{\text{y = 80}}} \cr & 80{\text{x = 11520 }} \cr & \Rightarrow \boxed{{\text{x = 144}}} \cr & {\text{x - y = 144 - 80 = 64 Ans}}{\text{.}} \cr} $$