The sum of two numbers is 75 and their difference is 25. The product of the two numbers is :

Solution(By Examveda Team)

Let the numbers be a and b
According to the question,
$$\eqalign{ & a + b = 75 \cr & a - b = 25 \cr & \because {\left( {a + b} \right)^2} - {\left( {a - b} \right)^2} = 4ab \cr & \Rightarrow {75^2} - {25^2} = 4ab \cr & \Rightarrow 4ab = \left( {75 + 25} \right)\left( {75 - 25} \right) \cr & \left[ {\because {a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)} \right] \cr & \Rightarrow 4ab = 100 \times 50 \cr & \Rightarrow ab = \frac{{100 \times 50}}{4} \cr & \Rightarrow ab = 1250 \cr} $$