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?

A covers an angular distance of 180 degrees (half a circle) to reach the point diametrically opposite to his starting point. B starts 30 degrees ahead of A. When A reaches the 180-degree mark, B also reaches the same 180-degree mark. Therefore, B covers an angular distance of (180 - 30) = 150 degrees. Since both A and B run for the same amount of time until they meet, the ratio of their speeds is equal to the ratio of the angular distances they covered. Ratio of speeds (A : B) = Angular distance covered by A : Angular distance covered by B = 180 : 150 Simplifying the ratio by dividing both sides by 30: = 6 : 5.

Thus, the ratio of speeds of A and B is 6:5.

Option Analysis: A) 6:5: This is the correct ratio derived from the angular distances covered by A (180 degrees) and B (150 degrees). B) 4:3: Incorrect. This ratio does not match the calculated angular distances. C) 6:1: Incorrect. This would imply B covered only 30 degrees while A covered 180 degrees, which is not the case. D) 4:2: Incorrect. This simplifies to 2:1, which is not the correct ratio.

The final answer is A.