The product of two numbers is 120 and the sum of their square is 289. The sum of the numbers is :

Answer: Option B

Let the numbers be x and y
Then,
xy = 120 and x² + y² = 289
$$\begin{array}{rl}& \therefore {\left(x+y\right)}^2\\ & =x^2+y^2+2xy\\ & =289+240\\ & =529\\ & \therefore x+y\\ & =\sqrt{529}\\ & =23\end{array}$$