Question : If $x:y=2:1$, then $(x^{2}-y^{2}) : (x^{2}+y^{2})$ is:
Option 1: 3 : 5
Option 2: 5 : 3
Option 3: 4 : 5
Option 4: 5 : 6
Correct Answer: 3 : 5
Solution : $x : y = 2 : 1$ Let $x = 2k$ and $y = k$ So, $x^2 = 4k^2$ and $y^2 = k^2$ Now putting the value in the given equation, we get, $(x^{2}-y^{2}) : (x^{2}+y^{2})$ $= (4k^2 - k^2) : (4k^2 + k^2)$ $= 3k^2 : 5k^2=3:5$ Hence, the correct answer is 3 : 5.
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