A : B = 160 : 150, A : C =160 : 130
B/C = (B/A) x (A/C) = (150/160) x (160/130) = 15/13 = 60 : 52
? In a game of 60, B can give C = (60 - 52)= 8 points
Clearly, Yogesh beats vijay by 20 s.
Distance covered by vijay in 400 s = 1000 m
[? 6 min 40 s = 400 s]
Distance covered by Vijay in 20 s = (1000/400) x 20 m = 50 m
? Yogesh beats Vijay by 50 m.
Time taken by L to run 1 km = 600 s
Time taken by M to run 1 km = 720 s
? L can give M a start of (720 - 600) = 120 s
? In 720 s, M runs 1000 m.
In 120 s M runs = (1000/720) x 120 = 500/3 m = 1662/3 m
Hence, L can give a start of 1662/3 m
Clearly, X beats Y by 8 s.
Distance covered by Y in 600 s = 1000 m
(? 10 min = 600 s)
Distance covered by Y 80 s. = (1000/600) x 80 = 400/3 m = 1331/3 m
According to the formula,
Time taken by the winner/Distance covered by the loser = Difference of winning time/ Difference of winning distance
? Time taken by P//(1000 - 72) = 12/72
? Time taken by P = (12/72) x 928
= 464/3 = 1542/3 s
To reach the winning post, A has to cover (250 - 140)m = 110 m
From the the ratio of 1 : 2 ,
When A covers 1m, then B covers 2 m.
When A covers 110 m, then B covers
( 2 x 110)m = 220 m
? A wins by (250 - 220) = 30 m
According to the question, A : B = 200 : 150
and B : C = 200 : 192
? A : C = (A/B) x (B/C) = (200/150) x (200/192) = 200/144
So, A beats C by (200 - 177) = 56 m
A : B = 200 : 160
A : C = 200 : 144
? B/C = (B/A) x (A/C) = (160/200) x (200/144)
= 160/144 = 10/9 = 200/180
Hence, B can give C 20 points
Distance covered by B in 27 seconds = 100 x 27 / 30 = 90 m
Hence, A will beat B by (100 ? 90) = 10 m.
To reach the winning post B will have to cover the distance (440 ? 40) = 400 m.
Hence,
time taken by B to cover 440 meter = 55
time taken by B to cover 1 meter = 55 / 440
time taken by B to cover 400 meter = 400 x 55 / 440 = 40 x 55/44 =10 x 55/11 = 10 x 5
time taken by B to cover 400 meter = 50 Sec.
Since, A reaches the winning post in 51 sec. while B in 50 sec.
So, B will win by 1 second.
? B runs 1000 m while C 960 m
? B runs 995 m while C 960 * 995 / 1000 = 912 m
Now, A runs 1000 m while C 960 m
? A runs 2000 m while C 2000 * 912 / 1000 = 1824 m
Hence, A can give C (2000 ? 1824) = 176 m start.
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