If $x + 2 y : 2 x - y$ is the duplicate ratio of $3 : 2$ , find the value of $x : y$ .

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Solution

Calculation of the ratio $x : y$ :
For the ratio $x : y$ , the duplicate ratio is $x^{2} : y^{2}$ .
So, the duplicate ratio of $3 : 2$ is $9 : 4$ .
$\Rightarrow x + 2 y : 2 x - y = 9 : 4 \Rightarrow \frac{x + 2 y}{2 x - y} = \frac{9}{4} \Rightarrow 4 (x + 2 y) = 9 (2 x - y) (C r o s s m u l t i p l y i n g b o t h s i d e s) \Rightarrow 4 x + 8 y = 18 x - 9 y \Rightarrow 18 x - 4 x = 9 y + 8 y (S e p a r a t i n g t h e v a r i a b l e s) \Rightarrow 14 x = 17 y ∴ \frac{x}{y} = \frac{17}{14} (D i v i d i n g b o t h s i d e s b y 14 y)$
Final Answer: The ratio $x : y$ is $17 : 14$ .

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