Formula for Average Speed: Average Speed = Total Distance / Total Time

Total Distance: Total Distance = $4d$ (as there are 4 legs of the journey)

Total Time:

Time for the first leg (X to Y) = $d / V$ Time for the second leg (Y to X) = $d / (2V)$ Time for the third leg (X to Y again) = $d / (3V)$ Time for the fourth leg (Y to X again) = $d / (4V)$ Total Time = $(d/V) + (d/2V) + (d/3V) + (d/4V)$

Simplifying Total Time: Total Time = $d/V * (1 + 1/2 + 1/3 + 1/4) = d/V * 25/12$

Average Speed: Average Speed = $4d / (d/V * 25/12) = (4d * 12V) / (25d) = 48V / 25 \approx 1.92V$

The average speed lies between V and 2V.

Thus, Option B is the correct answer.