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

Sum

If (x + 2y) : (2x – y) is equal to the duplicate ratio of 3 : 2

then `(x + 2y)/(2x - y) - (3)^2/(2)^2 = (9)/(4)`

⇒ 9(2x - y) = 4(x + 2y)
⇒ 18x - 9x = 4x + 8y
⇒ 18x - 4x = 8y + 9y
⇒ 14x - 17y
⇒ `x/y = (17)/(14)`
∴ x : y = 17 : 14.

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