If x : 6 ∷ 6 : y, and x : y ∷ y : 6, then which of the options below given the correct values of x and y, in that order?

Correct option is A

Given:

​$$x : 6 :: 6 : y$$ and $$x : y :: y : 6$$​​

Solution:

According to given information

​$$\frac{x}{6}= \frac{6}{y}$$ =  x $$\times$$y = 36 --------(Equation-1)

Again;

​$$\frac{x}{y} = \frac{y}{6}$$ = y² = 6x ------------(Equation- 2)

From( equation- 1) x = $$\frac{36}{y}$$​​

Put in the value of x in equation -2 

x² = 6$$\times$$​ $$\frac{36}{y}$$ = y³ = 216

$$y = \sqrt[3]{216} = 6$$​​

Again put in the value of y in equation 1 

x = 6

Thus the correct answer is (A)

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