The difference between two positive integers is 3. If the sum of their squares is 369, then the sum of the numbers is :

A. 25

B. 27

C. 33

D. 81

Answer: Option B

Solution(By Examveda Team)

Let the numbers be x and (x + 3)
Then,
$$\eqalign{ & \Leftrightarrow {x^2} + {\left( {x + 3} \right)^2} = 369 \cr & \Leftrightarrow {x^2} + {x^2} + 9 + 6x = 369 \cr & \Leftrightarrow 2{x^2} + 6x - 360 = 0 \cr & \Leftrightarrow {x^2} + 3x - 180 = 0 \cr & \Leftrightarrow \left( {x + 15} \right)\left( {x - 12} \right) = 0 \cr & \Leftrightarrow x = 12 \cr} $$
So, the numbers are 12 and 15
∴ Required sum = (12 + 15) = 27