​The sum of two numbers is 27 and the difference of their squares is 243. What is the difference between the numbers?​

Correct option is A

Given:

The sum of two numbers: a + b = 27 

The difference of their squares: $$a^2 - b^2$$ = 243

Concept used:

Use the identity for the difference of squares: 

​$$a^2-b^2$$ = (a + b)(a−b)

​Solution: 

difference of squares: 

​$$a^2-b^2$$ = (a + b) (a−b)

243 = (27) (a−b) 

(a−b) = $$\frac{243}{27}$$ = 9

​The difference between the two numbers is 9 

Thus, correct answer is (a) 9