The difference between two positive integers is 3. If the sum of their squares is 369, then the sum of the numbers is :

Answer: Option B

Let the numbers be x and (x + 3)
Then,
$$\begin{array}{rl}& \iff x^2+{\left(x+3\right)}^2=369\\ & \\ & \iff x^2+x^2+9+6x=369\\ & \iff 2x^2+6x-360=0\\ & \iff x^2+3x-180=0\\ & \iff \left(x+15\right)\left(x-12\right)=0\\ & \iff x=12\end{array}$$
So, the numbers are 12 and 15
∴ Required sum = (12 + 15) = 27