Question

The difference of the squares is of two numbers is 80% of the sum of their squares The ratio of the larger number to the smaller number is

• A. 5 : 2
• B. 2 : 5
• C. 3 : 1
• D. 1 : 3

Answer 1

The correct option is C 3 : 1

Let the two numbers be x and y Then $x^2-y^2=80\%$ of $(x^2+y^2)$
$\Rightarrow x^2-y^2=\frac{4}{5}(x^2+y^2)\Rightarrow x^2-\frac{4}{5}{x}^2=\frac{4}{5}{y}^2+y^2$
$\Rightarrow \frac{1}{5}{x}^2=\frac{9}{5}{y}^2\Rightarrow \frac{x^2}{y^2}=\frac{9}{1}\Rightarrow \frac{x}{y}=\frac{3}{1}\Rightarrow x:y=3:1$