# The Sum of Two Numbers is 37 and the Difference of Their Squares is 185 :

The sum of two numbers is 37 and the difference of their squares is 185, then the difference of the two numbers is:

- 3
- 10
- 4
- 5

**Answer: (4) 5**

**Explanation:-**

Let the two numbers be X and Y

The sum of two numbers is 37,

Then, X + Y = 37 …………………………….. (1)

The difference of their squares is 185.

Then, X² – Y² = 185 …………………. (2)

X² – Y² = (X – Y) (X + Y)

From equation (1) and (2),

185 = (X – Y) x 37

X – Y = 185/37

X – Y = 5

Then, the difference of two numbers is 5.

Hence, the answer is (4) 5.