Ratio of the speeds of A and B =5 : 1 = 5 :3
Thus, in race of 5 m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
80 m will be gained by A in race of m =200m
=> Winning post is 200 m away from the starting point.
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C
= (600 x 212.5)/1000 = 127.5 m.
A : B = 60 : 45.
A : C = 60 : 40.
B/C = (B/A*A/C) = (45/60*60/45) = 45/40 = 90/80 = 90:80
B can give C 10 points in a game of 90.
B runs 35 m in 7 sec.
B covers 200 m in (7/35*200) = 40 sec.
B's time over the course = 40 sec.
A's time over the course (40 - 7) sec = 33 sec.
To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.
While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers (4/3)*360 = 480 m.
Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
A wins by 20 m.
Distance covered by B in 9 sec. = (100/45)*9m = 20m
A beats B by 20 metres.
A : B = 200 : 169.
A : C = 200 : 182.
C/B = (C/A*A/B) = (182/200*200/169) = 182:169
When C covers 182 m, B covers 169 m.
When C covers 350 m, B covers (169/180*350)m = 325 m
Therefore, C beats B by (350 - 325) m = 25 m.
When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters.
Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters.
So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C.
So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters.
A : B = 100 : 75
B : C = 100 : 96.
A : C = (A/B*B/C) = (100/75*100/96) = 100/72 =100:72
A beats C by (100 - 72) m = 28 m.
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