Which information are necessary to answer the questions asked- In a kilometer race, by how many meters Rakesh beats Amit? Statement I : In a kilometer race, Rakesh beats Chand by 200 meters. Statement II : The respective ratio of the speed of Amit and Chand is 4: 3. Statement III : In a kilometer race, Amit beats Chand by 150 meters.

Statement I: Rakesh beats Chand by 200m in 1km, so when Rakesh finishes 1000m, Chand runs 800m. Speed ratio R:C = 1000:800 = 5:4. Statement III: Amit beats Chand by 150m, so when Amit finishes 1000m, Chand runs 850m. Speed ratio A:C = 1000:850 = 20:17. Statement II: A:C = 4:3 = 20:15. Using I and III: R:C = 5:4 and A:C = 20:17, we can find R:A and then the beat distance. Using II and I: C:A = 3:4 and R:C = 5:4 gives R:A = 15:16, so Amit covers 16/15 of Rakesh's distance in same time. In 1000m, Rakesh beats Amit by (16-15)/15 × 1000 = 66.67m. Using II and III: A:C = 4:3 and A:C = 20:17 contradiction means one must be wrong, but if we trust both as scenarios, we can still solve. Any two statements give sufficient information.