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

Given that the sum of two numbers is 40 and their difference is 4

Suppose that $x,y$ are two numbers

$x+y=40,x-y=4$

Adding the above two equations $2x=44\Rightarrow x=22$

substitute $x=22$ in any one of the equations, we get 

$\begin{array}{rcl}22+y& =& 40\\ y& =& 40-22\\ & =& 18\end{array}$

Therefore, the ratio of the above two numbers is $\frac{22}{18}=\frac{11}{9}$