A circular path is 800 m long. Beena and Arun run in opposite directions from the same point A on the path at the same time. They continue to run after they meet for the first time. Beena runs another 53(1/3) seconds to arrive at A, while Arun runs another 2 minutes to get to point
A. Which of the following statements is/are correct? Statement I: The speed of Beena is 6 m/sec. Statement II: The ratio of the speeds of Arun and Beena is 2 : 3.

Beena takes 53(1/3) seconds to run from the meeting point back to point A. Since the path is circular, this distance is half the total length of the path (since they meet after running halfway around). Therefore, the distance Beena covers after the meeting is... Distance =800 /2 =400 meters Speed of Beena = Distance /Time = 400 / (160/ 3) = (400 x 3)/160 = 7.5 m/sec Thus, Statement I is incorrect, as Beena's speed is 7.5 m/sec, not 6 m/sec. Arun takes 2 minutes (or 120 seconds) to run from the meeting point back to point A. The distance Arun covers after the meeting is also 400 meters.   Arun's speed = 400 /120 =10/3 Speed of Arun = 10/3m/sec ≈ 3.33 m/sec The ratio of speeds = Speed of Arun: Speed of Beena =10 /3:7.5 =10:22.5 =100:225 =4:9 Thus, Statement II is also incorrect, as the ratio of the speeds of Arun and Beena is 4: 9, not 2: 3.