If y/(x - z) = (y + x)/z = x/y then find z : y : x ?

Q: If y/(x - z) = (y + x)/z = x/y then find z : y : x ?

Given, y/(x - z) = (y + x)/z = x/y y z = x y + x 2 - y z - x z . . . . ( 1 ) Also x y = y x - z ⇒ x 2 - x z = y 2 . . . . ( 2 ) Using (1) and (2), we get yz = xy - yz + y 2 2yz = xy + y 2 2z = x + y Only option (B) satisfies the equation.

1:2:3
3:2:4
4:3:2
2:3:4

Correct Answer: 3:2:4

Explanation:

Given, y/(x - z) = (y + x)/z = x/y
$y z = x y + x 2 - y z - x z . . . . (1)$
Also $\frac{x}{y} = \frac{y}{x - z}$ $\Rightarrow x 2 - x z = y 2 . . . . (2)$
Using (1) and (2), we get yz = xy - yz + $y 2$
2yz = xy + $y 2$
2z = x + y
Only option (B) satisfies the equation.

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