If the third proportion of 3 and x is 27 and the third proportion of 2 and y is 8, then find x : y.

Correct option is C

Formula Used:
The formula for the third proportion is:
$$\frac{a }{ b }= \frac{ b }{c}$$​, which implies that $$c = \frac{b^2 }{ a}$$​​

Solution:

Apply the formula to find x:
For the third proportion of 3 and x, we have:
​$$\frac{3 }{ x} =\frac{ x }{ 27}$$​​
Cross-multiply: $$x^2 = 3 × 27 = 81$$​​
Therefore, x = √81 = 9.
Apply the formula to find y:
For the third proportion of 2 and y, we have:
​$$\frac{2 }{ y }= \frac{y }{8}$$​​
Cross-multiply: $$y^2 = 2 × 8 = 16$$​​
Therefore, y = √16 = 4.
Find the ratio x : y:
Now that we have x = 9 and y = 4, the ratio x : y is:
x : y = 9