Calculating distance from VOR station with radial and heading
Bad news: the question is unanswerable.
Good news: you're right to be confused!

With a groundspeed of 120 knots and a constant ground track, after 10 minutes the airplane will have moved 20 miles in a straight line. There's no getting around this fact.

If the airplane doesn't parallel a radial, and yet it moves, the radial it's on must change.

If it's still indicating the same radial after non-parallel movement, the only option is that the indicator is in error.  But the question removes that possibility.

The only way I can think to make this situation possible is that maybe you've tuned the world's most bizarre VOT. But even still there's no possibility for a valid answer for the question.


The original question:

At time t(1) an airborne VOR receiver shows that the aircraft is on the 30deg radial from a VOR station. The pilot maintains a ground track heading of 120deg with respect to magnetic North and 120 knots ground speed. At time t(2) , 10 minutes later than t(1) , the VOR receiver indicates that the aircraft is on the 30deg radial from the same station. Assuming no errors, what is the pilot’s distance from the VOR station at time t(2) ? If the pilot had access to airspeed, can the range be determined from the VOR measurements? Can it be determined if the pilot had access to ground speed and ground track heading?