The ratio of third proportional to 12 and 18 and the mean proportional of 3 and 12 is

A 2 : 9

B 9 : 2

C 3 : 8

D 8 : 3

E None of these

Correct Answer: Option B

Let the third proportional of 12 and 18 be x

\(\therefore \frac{{12}}{{18}} = \frac{{18}}{{\rm{x}}}\)

⇒ 12 × x = (18 × 18)

⇒ 12x = 324

⇒ x = 27

Now, let the mean proportional of 3 and 12 be y

\(\therefore {\rm{\;}}\frac{3}{{\rm{y}}} = {\rm{\;}}\frac{{\rm{y}}}{{12}}\)

⇒ y × y = 3 × 12

⇒ y² = 36

⇒ y = 6

∴ The ratio x : y = 27 : 6

⇒ Ratio = 9 : 2