If 12 : x :: x : 27, and 25 : y :: y : 36, when x and y are both positive numbers, find x : y

Correct option is B

Given:

​$$12:x::x:27,$$ And  $$25:y::y:36$$​​

Solution:

The proportion is

​$$\frac{12}{x} = \frac{x}{27},$$  And  $$\frac{25}{y} = \frac{y}{36}$$

From the proportion, 

$$\frac{12}{x} = \frac{x}{27},$$​​

$$12 \cdot 27 = x^2$$ 

$$x^2 = 324$$ 

​$$x = \sqrt{324} = 18$$ 

And, from the proportion ,$$\frac{25}{y} = \frac{y}{36}$$

$$25 \cdot 36 = y^2$$

$$y^2 = 900$$ 

$$y = \sqrt{900} = 30$$ 

$$x : y = 18 : 30$$

$$x : y = \frac{18}{6} : \frac{30}{6} = 3 : 5$$

$$x : y = 3 : 5$$ 

Thus the correct answer is (B)