A car travels from a place X to place Y at an average speed of V km/hr

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

1. is less than v km/hr
2. lies between v and 2v km/hr
3. lies between 2v and 3v km/hr
4. lies between 3v and 4v km/hr

• Answer: The correct option is B
• Explanation:

  Let the distance between X and Y be 12 km and v = 1 km/hr.

  Time taken = Distance/Speed

  Time taken in 1st journey = 12/v = 12/1 = 12 hr

  Time taken in 2nd journey = 12/2v = 12/2 = 6 hr

  Time taken in 3rd Journey = 12/3v = 12/3 = 4 hr

  Time taken in 4th Journey = 12/4v = 12/4 = 3 hr

  Now, total distance = 12 × 4 = 48 km

  Average Speed = (Total Distance)/(Total Time)

  = 48/(12 + 6 + 4 + 3)

  = 48/25 (this value lies between 1 and 2)

  So, the average speed of the car for the entire journey lies between v and 2v.

• Exam Year: 2020