The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is :

Answer: Option A

Let the numbers be x and y
Then,
$$\begin{array}{rl}& \iff \frac{x+y}{x-y}=\frac{40}{4}\\ & \iff \frac{x+y}{x-y}=10\\ & \iff \left(x+y\right)=10\left(x-y\right)\\ & \iff 9x=11y\\ & \iff \frac{x}{y}=\frac{11}{9}\\ & \iff x:y=11:9\end{array}$$