# The Product of the Two Numbers is :

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

- 1000
- 1350
- 1250
- 125

**Answer: (3) 1250 **

**Explanation:-**

Let the two numbers be X and Y.

The sum of two numbers is 75

Then, X + Y = 75 …………………………. (1)

The difference two numbers is 25

Then, X – Y = 25 ………………………… (2)

**As we know that, (X + Y)² – (X – Y)² = 4 X Y**

Now, From equation (1) & (2),

75² – 25² = 4 X Y

5000 – 625 = 4 X Y

5000 = 4 X Y

X Y = 5000/4

X Y = 1250

Then, the product of the numbers is 1250.

Hence, the answer is (3) 1250.