puzzles - lokesh bidhu and lavish are participating in a race of 100 meters bidhu is beaten by lokesh by 20 meters lavish is beaten by bidhu by 20 meters how many meters does lokesh beat lavish by - skillgun

It is tempting to guess that Lokesh beats Lavish by 40 meters, but when Lokesh finishes and is 20 meters ahead of Bidhu, Bidhu is NOT 20 meters ahead of Lavish (he's only 16 meters ahead), and it will take a couple more seconds before Bidhu increases his lead over Lavish to 20 meters.
To figure out the answer, we let Lokesh speed be A meter/second. So it takes him 100/A seconds to finish the race. At this point, we know that Bidhu has run 80 meters (since Lokesh beats him by 20 meters). So Bidhu runs 80 meters in 100/A seconds, meaning that he is running at a speed of (80/(100/A)) meters/second, or (8A/10) meters per second.
So we then know that it takes Bidhu 100/(8A/10) seconds to finish the race, or 125/A seconds. At this point, we know that Lavish has run 80 meters (since Bidhu beats him by 20 meters). So Lavish runs 80 meters in 125/A seconds, meaning that he is running at a speed of (80/(125/A)) meters/second, or 80A/125 meters per second.
Now that we know Lavish's speed, we just need to figure out how far he had run when Lokesh finished the race. Since Lokesh finished in 100/A seconds, we can determine that Lavish had run (100/A) * (80A/125) = 8000/125 = 64 meters when Lokesh finished the race. And so Lokesh beat him by (100 - 64) = 36 meters.