Question

The sum of two numbers is 18 and the difference of their squares is 108 The difference between the numbers is

• A. 2
• B. 12
• C. 6
• D. 8

Answer 1

Answer: (C)

6

Let one number be $x$
Then other number $=18-x$
Given $(18-x{)}^2-x^2=108$
$\Rightarrow 324-36x+x^2-x^2=108$
$\Rightarrow 36x=324-108=216$
$\Rightarrow x=\frac{216}{36}=6$
$\therefore$ The difference between the two numbers
$=18-x-x$
$=18-2x=18-2\times 6$
$=18-12=6$