X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3:2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?

Correct Option: 3

Length of circular course = 300 m = 0.3 km. Total race distance = 3 km. Ratio of speeds of X and Y = 3 : 2. Since they run in the same direction, the relative speed in terms of completing laps is the difference in their speeds ratio or lap difference per unit time. X runs 3 km in total, which is 3000 / 300 = 10 laps. Y runs at speed ratio 2, so Y completes 10 x (2/3) = 6.67 laps. The number of times the faster runner passes the slower runner in the same direction during a race is given by the difference in the number of laps completed by them. Number of laps by X = 10. Number of laps by Y = 10 x (2/3) = 20/3 = 6.67 laps. Wait, let us use the relative distance formula: Relative speed = 3v - 2v = v. In 3 km, the number of full passes is calculated by dividing total distance by the circular track length when speeds are proportional, or simply: Difference in laps = 10 - 20/3 = 10/3 = 3.33. Since passing only counts when complete, the first runner passes the other 3 times before the finish line (excluding the start). Thus, option B is correct.