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
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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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