A is faster than B. In a 2500 m race, A gives B a start of 200 meters. A runs at 25 m/s. Who wins and by how much if B runs at 23 m/s?

The correct option is They finish together.

Let us analyze the race step-by-step to understand why both A and B reach the finish line at the exact same time.
First, let's identify the total length of the race track, which is 2500 meters.

1. Distance to be covered by Runner A:
Since A starts from the beginning of the race track, A has to run the entire distance of the race.
Distance covered by A = 2500 meters.
The speed of A is given as 25 m/s.

We can calculate the time taken by A to finish the race using the formula:
Time = Distance / Speed

${\mathrm{Time}}_A=\frac{2500m}{25\mathrm{m/s}}=100\mathrm{seconds}$

So, A takes 100 seconds to reach the finish line.

2. Distance to be covered by Runner B:
A gives B a head start of 200 meters. This means B starts 200 meters ahead of the starting line.
Distance covered by B = Total race distance - Head start
Distance covered by B = 2500 meters - 200 meters = 2300 meters.
The speed of B is given as 23 m/s.

We can calculate the time taken by B to finish the race using the same formula:
Time = Distance / Speed

${\mathrm{Time}}_B=\frac{2300m}{23\mathrm{m/s}}=100\mathrm{seconds}$

So, B also takes 100 seconds to reach the finish line.

Conclusion:
Since both A and B take exactly 100 seconds to reach the finish line, neither of them beats the other. Therefore, they finish the race together.