In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speeds of A to B assuming that both start at the same time?

To find the ratio of speeds, we need to determine the distance covered by A and B in the same amount of time. 1. Distance covered by A: A runs the entire race, so A covers 500 metres. 2. Distance covered by B: * B starts 45 metres ahead of A. This means B's initial position is at 45m from the starting line. * A wins the race, and at that moment, B is 35 metres behind A. Since A finished at 500m, B's position at that time is 500 - 35 = 465 metres from the starting line. * The actual distance B covered is B's final position minus B's initial position: 465m - 45m = 420 metres. Since both start at the same time and A finishes while B is at a certain point, the time taken by both to cover their respective distances is the same. When time is constant, the ratio of speeds is equal to the ratio of distances covered. Ratio of speeds (A to B) = Distance covered by A : Distance covered by B Ratio = 500 : 420 Simplify the ratio: Divide both numbers by 10: 50 : 42 Divide both numbers by 2: 25 : 21 Therefore, the ratio of the speeds of A to B is 25:21. The final answer is A) 25:21.