Let assume the game has P points.
Then A has P points , B has (P ? 15) and C has (P ? 22) points and also if B has P points then C has (P ? 10) points.
Applying chain rule,
P x P ( P ? 22 ) = P ( P ? 15) ( P ? 10)
? P² ? 22P = P² ? 25P + 150
? 3P = 150
? P = 50

? B scores 75 points while A 80
? B scores 60 points while A = 80 x 60 / 75 = 64
Again, A scores 80 points while C = 65
? A scores 64 points while C = 65 x 64 / 80 = 52 points
Hence, in a game of 60, B can give C (60 ? 52) = 8 points

Here, A will have to cover a distance of (500 ? 140) = 360 meters to reach the winning point while B 500 meters . A covers 3 while B covers 4.
? A covers 360 m while B covers 4 x 360/ 3 = 480 m
Hence, B will be (500 ? 480) = 20 m behind the winning post.
? A wins by 20 m.

Clearly, if A runs 600 meters, B runs = 540 m.
? If A runs 400 m, B runs = 540 x 400 / 600 = 540 x 4 / 6 = 90 x 4 = 360 m
Again, when B runs 500 m, C runs = 450 m
? When B runs 360 m, C runs = 450 x 360 / 500 = 45 x 36 / 5 = 9 x 36 = 324 m.
? A beats C by 400 - 324 = 76 m.

If A runs 600 m, B runs 600 - 60 or, 540 m.
If A runs 400 m, B runs = 540 x 400 / 600 = 360 m.
Now, when B runs 500 m, C runs 500 - 50 = 450 m.
? When B runs 360 m, C runs = 450 * 360 / 500 = 324 m
? A beats C by 400 - 324 = 76 m.

When A scores 75 points, B scores 50 points.
When A scores 90 points, C scores (90 - 18) = 72 points.
? When A scores 75 points, C scores = 72 × 75 / 90 = 60 points.
A : B : C = 75 : 50 : 60
C : B = 60 / 50 = 120 / 100
So, in a game of 120, C can give B
(120 - 100) = 20 points.

To reach the winning post, A will have to cover a distance of (500 - 140). i.e, 360 m.
While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers 4 × 360 / 3 = 480 m.
So, A reaches the winning post while B remains 20 meter behind.
? A wins by 20 m.

Speeds (in m/sec) of A and B are
9 / 2 * 5 / 18 = 5 / 4 and 6 * 5 / 18 = 5 / 3, respectively.
A has a start of 190 m.
So, A has to run 1000 - 190 = 810 m, while B 1000 m.
Time taken by B to cover 1000 m = 3 5 × 1000 = 600 seconds.
In this time, A covers 5 × 600 / 4 = 750 m.
So, B reaches the winning post while A remains 810 - 750 = 60 m behind.
? B wins by 60 m.

A's speed = (5 * 5 / 18) m/sec = 25 / 18 m/sec
Time taken by A to cover 100 m = (100 * 18 / 25) sec = 72 seconds.
? B covers 92 m in 72 + 8 = 80 seconds.
B's speed = (92 / 80 * 18 / 5) Km/h = 4.14 Km/h.

A will reach at starting point in 5 * 2 / 5 = 2 hours ;
B will reach at starting point in 5 / 3 hours ;
C will reach at starting point in 5 / 2 hours ;
Then, on the starting point all three will meet after the L.C.M. of 2, 5 / 3, 5 / 2, 10 / 1 = 10 hours.