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
(a) Is less than v km/hr
(b) Lies between v and 2v km/hr
(c) Lies between 2v and 3v km/hr
(d) Lies between 3v and 4v km/hr
Correct Answer: (b) Lies between v and 2v km/hr
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Car travels from place x to place y
Let’s say the distance between place X and place Y is D km. The total distance traveled by the car during its entire journey would be (4 * D) = 4D km.
The time taken for each leg of the journey would be:
From X to Y: D/v hours
From Y to X: D/(2v) hours
From X to Y: D/(3v) hours
From Y to X: D/(4v) hours
So the total time taken for the entire journey would be (D/v + D/(2v) + D/(3v) + D/(4v)) = (25D/12v) hours.
Therefore, the average speed of the car for the entire journey would be (total distance)/(total time) = (4D)/(25D/12v) = (48/25)v.
This value lies between v and 2v, so the correct answer is indeed (b) Lies between v and 2v km/hr.
