Hello, hisajesh!

A can beat B by 20 yards in a 200-yard race.

B can beat C by 10 yards in a 250-yard race.

By how many yards can A beat C in a 100-yard race?

Let

In the time A has run 200 yards, B has run only 180 yards.

B's speed is of A's speed: . .[1]

In the time B gas run 250 yards, C has run only 240 yards.

C's speed is of B's speed: . .[2]

Substitute [1] into [2]: .

. . That is, C's speed is of A's speed.

When A has run 100 yards, C has run only yards.

Therefore, A wins by yards.