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Mathematics

If (x + 2y) : (2x - y) is equal to the duplicate ratio of 3 : 2, find x : y.

Ratio Proportion

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Answer

Duplicate ratio of 3 : 2 = 32 : 22 = 9 : 4.

According to question,

(x + 2y) : (2x - y) = 9 : 4

⇒x+2y2x−y=94⇒4(x+2y)=9(2x−y)⇒4x+8y=18x−9y⇒4x−18x=−9y−8y⇒−14x=−17y⇒xy=−17−14⇒xy=1714⇒x:y=17:14\Rightarrow \dfrac{x + 2y}{2x - y} = \dfrac{9}{4} \\[0.5em] \Rightarrow 4(x + 2y) = 9(2x - y) \\[0.5em] \Rightarrow 4x + 8y = 18x - 9y \\[0.5em] \Rightarrow 4x - 18x = -9y - 8y \\[0.5em] \Rightarrow -14x = -17y \\[0.5em] \Rightarrow \dfrac{x}{y} = \dfrac{-17}{-14} \\[0.5em] \Rightarrow \dfrac{x}{y} = \dfrac{17}{14} \\[0.5em] \Rightarrow x : y = 17 : 14

Hence, the value of x : y is 17 : 14.

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