More metres, More time (Direct Proportion)
∴ 0.128 : 25 :: 1 : x ⟺ 0.128x = 25 x 1
x = | 25 | = | 25 x 1000 |
0.128 | 128 |
⟹ x = 195.31.
∴ Required time = 195 sec (approximately).
Let the trains meet after time t at a distance x from station N.
Then another train coming from station M covers a distance of (x + 50)
For station M,
(x + 50) = 125t
? x = 125t - 50 ..(i)
For station N,
x = 75t .....(ii)
From Eqs. (i) and (ii), we get
75t = 125t - 50
? t = 1h
Distance between station M and N = 125 + 75t = 200 x 1 = 200 km
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.
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.
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.
Let the speeds of two trains be x and y, respectively .
? Length of 1st train = 54x
Length of the 2nd train = 34y
According to the question.
(54x + 34y) / (x + y) = 46
? 54x + 34y = 46x + 46y
? 27x + 17y = 23x + 23y
? 4x = 6y
? x/y = 3/2
? x : y = 3 : 2
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 runs 1000 meters while B runs 900 meters and C runs 800 meters.
Therefore, B runs 900 meters while C runs 800 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 800)/900 = 8000/9 = 888.88 meters
Thus, B can give C (1000 - 888.88) = 111.12 meters start
A : B = 100 : 80.
A : C = 100 : 72.
B:C = B/A*A/C = 80/10*100/72 = 10/9 = 100/90 = 100:90
B can give C 10 points
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