The ratio between the third proportional of 12 and 30 and mean proportional of 9 and 25 is -

Answer: Option B

Let the third proportional to 12 and 30 be x.
Then,
$$\begin{array}{rl}& =12:30::30:x\\ & \Rightarrow 12x=30\times 30\\ & \Rightarrow x=\frac{\left(30\times 30\right)}{12}=75\end{array}$$
∴ Third proportional to 12 and 30 = 75
Mean proportional between 9 and 25
$$\begin{array}{rl}& =\sqrt{9\times 25}=15\\ & \therefore \text{Required ratio}=75:15\\ & =5:1\end{array}$$