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

Solution (By Examveda Team)

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