What is the ratio of the volume of the given right circular cone to the one obtained from it?
I. The smaller cone is obtained by passing a plane parallel to the base and dividing the original height in the ratio 1 : 2.
II. The height and the base of the new cone are one-third those of the original cone.

Considering 1st statement alone:
As height is reduced to 1/3rd of it, radius will also get reduced 1/3rd of complete cone
Now we know volume is directly proportional to product of square of radius and height , we can calculate ratio of volumes.
Similarly considering 2nd statement alone, we can calculate ratio of volumes as we will have sufficient information regarding radius and height.
So answer will be B