Whose path is the longest: Uday, Kamala, or Meera?

Answer

To determine whose path is the longest among Uday, Kamala, and Meera, we need to analyze their movements on the circle. 1. **Uday's Path**: Uday picks the first ball and goes to another point on the circle. The distance covered can be visualized as an arc of the circle starting from the 'start' point to the 'end' point (point where he goes). This distance depends on the angle subtended by the two points he visits and is a part of the circumference of the circle. 2. **Kamala's Path**: Kamala starts from a different point and goes to the opposite point on the circle. This means she has picked a position that is directly across the circle from her start point. The distance she covers is essentially half of the circle's circumference, which is the longest possible distance on a circle, as it represents the maximum arc length. 3. **Meera's Path**: Meera also starts from a point on the circle, picks the third ball, and returns to her original position. This means her path is similar to that of Uday in terms of covering distance along the arc of the circle; however, since she returns to her starting point, the distance is the full arc length back, assuming only a single path to another point is compared. **Conclusion**: Since Kamala travels directly across the circle to the opposite side, she covers the longest path, which is exactly half of the circle. Uday and Meera's paths are shorter than Kamala's. Thus, Kamala has the longest path.