Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?

Correct Option: 6 : 5

Let the starting position of A be at 0 degrees on the circular track. Since B is ahead of A and their positions make an angle of 30 degrees at the center, B's starting position is at 30 degrees (running in the same direction). A reaches the point diametrically opposite to his starting point, which is at 180 degrees, where he meets B. During this time: The distance covered by A = 180 - 0 = 180 degrees. The distance covered by B = 180 - 30 = 150 degrees. Since both run for the same duration of time, the ratio of their uniform speeds is equal to the ratio of the angular distances they covered: Speed of A : Speed of B = Distance of A : Distance of B = 180 : 150 = 6 : 5. Thus, the ratio of their speeds is 6 : 5. Hence, option A is correct.