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 first 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 in the same time.

Since A has a start of 140 meters, this means that when B starts running, A has already covered 140 meters.

Let's assume that when A covers the remaining distance (500-140 = 360 meters), B covers 'x' meters.

Since the speeds of A and B are in the ratio 3:4, the distances covered by them would also be in the same ratio. Therefore, we can write the equation as:

360/x = 3/4

Solving this equation for 'x', we get:

x = (4 * 360) / 3 = 480 meters

This means that when A reaches the finish line, B has only covered 480 meters.

Therefore, A wins by a distance of 500 - 480 = 20 meters.