In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:

To solve this problem, we need to understand that the ratio of speeds of A and B is given as 3:4. This means that for every 3 meters that A runs, B runs 4 meters.

Step 1: Calculate the actual distance A runs A has a start of 140 meters, so the actual distance A runs is 500 - 140 = 360 meters.

Step 2: Calculate the distance B runs when A runs 360 meters Using the speed ratio 3:4, we can set up the proportion 3/4 = 360/x, where x is the distance B runs. Solving for x gives us x = (4 * 360) / 3 = 480 meters.

Step 3: Calculate how much B loses by B would have needed to run 500 meters to finish the race, but when A finishes, B has only run 480 meters. So, B loses by 500 - 480 = 20 meters.

So, A wins by 20 meters.