The sum of two numbers is 37 and the difference of their squares is 185, then the difference between the two numbers is :

Answer: Option C

Let the numbers be a and b, where a > b
According to the question,
$$\begin{array}{rl}& a+b=37\&a^2-b^2=185\\ & \Rightarrow \left(a+b\right)\left(a-b\right)=185\\ & \Rightarrow 37\left(a-b\right)=185\\ & \Rightarrow a-b=\frac{185}{37}\\ & \Rightarrow a-b=5\end{array}$$