Amit and Sumit are running a race of 100mtrs. When Amit gives Sumit a 10m headstart, he finishes 10m ahead of him. What will be the result when Amit gives Sumit a 20m headstart?

Scenario 1:
Amit travels 100 m
Sumit travels 80 m (10 m head start and 10 m lag at end)
as S is directly proportional to D.
Amit's speed = 5/4 Sumit's Speed
Scenario 2
Speed same , everything same headstart = 20 m
Again S directly proportional to D
So Amit travels 100m and Sumit 80.
So it's a tie.

Consider the first race: Amit covers 100m in the same time that Sumit takes to cover 80m. So, the ratio of speeds is 4:5.
In the second race also, they cover 100m and 80m in the same time. Since Sumit has a head-start of 20m, both of them reach the endpoint at the same time. So, it is a tie.