Q. A car travels from a place X to place Y at an average speed of v km/hr from y to X at an average speed of 2v km/hr, again from X to y at an average speed of 3v km/hr and again from y to x at an average speed of 4v km/hr. Then the average speed of the car for the entire journey

Explanation : 

Car travels from place x to y

Given: Car travels from X to Y multiple times
Distance: X to Y = D km
Total journey = 4 legs × D = 4D km

Time taken for each leg:
1. X to Y: D/v hours (speed = v)
2. Y to X: D/(2v) hours (speed = 2v)
3. X to Y: D/(3v) hours (speed = 3v)
4. Y to X: D/(4v) hours (speed = 4v)

Calculations:
1. Total Time = D/v + D/(2v) + D/(3v) + D/(4v)
= (12D + 6D + 4D + 3D)/(12v)
= 25D/(12v) hours

2. Average Speed = Total Distance/Total Time
= 4D/(25D/12v)
= (48/25)v km/hr
≈ 1.92v km/hr

Conclusion:
Since 48/25 is approximately 1.92:
v < (48/25)v < 2v

Therefore, answer is (b): Average speed lies between v and 2v km/hr.