If x : y = 4 : 15 then the value of ( x - yx + y ) is?

Answer: Option A

$$\begin{array}{rl}& y:x=4:15\\ & \therefore \frac{y}{x}=\frac{4}{15}\\ & \therefore \frac{x-y}{x+y}\\ & \Rightarrow \frac{x\left(1-\frac{y}{x}\right)}{x\left(1+\frac{y}{x}\right)}\\ & \text{Taking }x\text{ common}\\ & \Rightarrow \frac{1-\frac{4}{15}}{1+\frac{4}{15}}\\ & \Rightarrow \frac{11}{15}\times \frac{15}{19}\\ & \Rightarrow \frac{11}{19}\end{array}$$