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

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