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

Let the distance between X and Y be D km. 1. Total Distance: The car travels X to Y, Y to X, X to Y, and Y to X. So, it covers the distance D four times. Total Distance = D + D + D + D = 4D km. 2. Total Time: Time = Distance / Speed. Time for X to Y (speed v) = D/v Time for Y to X (speed 2v) = D/(2v) Time for X to Y (speed 3v) = D/(3v) Time for Y to X (speed 4v) = D/(4v) Total Time = D/v + D/(2v) + D/(3v) + D/(4v) To sum these fractions, find a common denominator, which is 12v. Total Time = (12D + 6D + 4D + 3D) / (12v) = 25D / (12v) hours. 3. Average Speed: Average Speed = Total Distance / Total Time. Average Speed = (4D) / (25D / 12v) Average Speed = 4D * (12v / 25D) Average Speed = (4 * 12v) / 25 Average Speed = 48v / 25 km/hr. 4. Evaluate the result: 48/25 = 1.92. So, the average speed is 1.92v km/hr. 5. Compare with options: A) is less than v km/hr (1.92v is not less than v) - Incorrect. B) lies between v and 2v km/hr (1v < 1.92v < 2v) - Correct. C) lies between 2v and 3v km/hr (1.92v is not between 2v and 3v) - Incorrect. D) lies between 3v and 4v km/hr (1.92v is not between 3v and 4v) - Incorrect. The average speed is 1.92v km/hr, which lies between v and 2v km/hr. The final answer is B