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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 journey1. is less than v km/hr2. lies between v and 2v km/hr3. lies between 2v and 3v km/hr 4. lies between 3v and 4v km/hr |
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Answer» Correct Answer - Option 2 : lies between v and 2v km/hr Given: Trip one X to Y with the speed of v km/h Trip one Y to X with the speed of 2v km/h Trip one X to Y with the speed of 3v km/h Trip one Y to X with the speed of 4v km/h Formula used: Average speed = Total distance covered/Total time taken Speed = Distance/Time Calculation: Let the distance between X and Y is a km Total distance covered = 4a ⇒ time = distance/speed Time is taken on the first trip ⇒ time = a/v Time is taken on the second trip ⇒ time = a/2v Time is taken on the third trip ⇒ time = a/3v Time is taken on the fourth trip ⇒ time = a/4v Total time = (a/v) + (a/2v) + (a/3v) + (a/4v) ⇒ (12a + 6a + 4a + 3a)/12v = 25a/12v Average speed = Total distance covered/Total time taken ⇒ 4a/(25a/12v) = 48v/25 ⇒ Average speed = 1.92v km/h ∴ Average speed of the car lies between v km/h and 2v km/h. |
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