In a race of 4 kms A beats B by 100 m or 25 seconds, then time taken by A is

Concept: When a problem states 'A beats B by x metres or t seconds' in a race, it means: at the instant A completes the race, B is still x metres short of the finish line, and B would need exactly t more seconds, running at B's own steady pace, to cover that remaining x metres. That relationship pins down B's speed as x ÷ t, since it is the extra distance B needed divided by the extra time B needed for it.

Application:

1. From the given gap, B's speed = 100 m ÷ 25 s = 4 m/s.

2. The race distance is 4 km = 4000 m, so B's time to cover the whole race at this speed is 4000 m ÷ 4 m/s = 1000 s, i.e., 16 minutes 40 seconds.

3. Since A finishes exactly 25 seconds before B (the same 25-second gap given in the question), A's time is 1000 s − 25 s = 975 s.

4. Converting 975 seconds: 975 ÷ 60 = 16 minutes with a remainder of 15 seconds, so A's time is 16 minutes 15 seconds.

Cross-check: This checks out: in 975 seconds A covers the full 4000 m, and in that same 975 seconds B (running at 4 m/s) covers 975 × 4 = 3900 m — exactly 100 m short of the 4000 m finish line, which matches the 100 m gap stated in the question.