The sum of two positive numbers is 27, while the difference of their squares is 81. What is the value of the greater of the two numbers?

Correct option is D

Given:

sum of two number only = 27

difference of their square = 81

Formula Used:

​$$x^2 - y^2 = (x - y)(x + y)$$

Solution;

​$$x + y = 27 \\x^2- y^2 = 81 \\x^2 - y^2 = (x - y)(x + y) \\(x - y)(27) = 81 \\x - y = \frac{81}{27} = 3 \\2x = 30 \\x = \frac{30}{2} = 15 \\y = 27 - 15 = 12$$ 

so the greatest number is =15