The sum of two numbers is 25 and their difference is 13. Find their product :

Answer: Option B

Let the numbers be x and y
Then,
x + y = 25 and x - y = 13
$$\begin{array}{rl}& \iff 4xy={\left(x+y\right)}^2-{\left(x-y\right)}^2\\ & \iff 4xy={\left(25\right)}^2-{\left(13\right)}^2\\ & \iff 4xy=625-169\\ & \iff 4xy=456\\ & \iff xy=114\end{array}$$