Question : If the third proportion of 3 and $x$ is 27 and the third proportion of 2 and $y$ is 8, then find $x : y$.
Option 1: 7 : 9
Option 2: 4 : 5
Option 3: 3 : 7
Option 4: 9 : 4
Correct Answer: 9 : 4
Solution :
If c is called the third proportional to a and b, then a : b = b : c
The third proportion of 3 and $x$ is 27.
So, $\frac{3}{x}=\frac{x}{27}$
$⇒x=\sqrt{3×27}$
$\therefore x = 9$
The third proportion of 2 and $y$ is 8.
So, $\frac{2}{y}=\frac{y}{8}$
$⇒y=\sqrt{2×8}$
$\therefore y = 4$
So, $x:y=9:4$
Hence, the correct answer is 9 : 4.
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