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

(c) 3 : 1

Let the two numbers be x and y.

Then, x²  - y² = 80% of (x² + y²)

\(\Rightarrow\) x² - y² = \(\frac{4}{5}\)(x² + y²) \(\Rightarrow\) x² - \(\frac{4}{5}\)x² = \(\frac{4}{5}\) y² + y²

\(\Rightarrow\)\(\frac{1}{5}\)x² = \(\frac{9}{5}\)y²  \(\Rightarrow\) \(\frac{X^2}{y^2}\) = \(\frac{9}{1}\) \(\Rightarrow\) \(\frac{X}{y}\)= \(\frac{3}{1}\) \(\Rightarrow\) x:y = 3:1