Question

train crosses two persons, cycling in the same direction as the train in 12 and 18 seconds respectively. If the speeds of the two cyclists are 9 and 18 kmph respectively, then find the length and speed of the train. (A) 80 m, 30 km/hr (C) 98 m, 36 km/hr (B) 89 m, 30 km/hr (D) 90 m, 36 km/hr

Answer 1

Let the length of train be 'L' m = Distance
Speed of train = S m/s
Speed of 1st cyclist = 9 km/hr = 9*5/18 = 2.5 m/s
Time to overtake him = 12 s
Relative speed = S - 2.5...[since, same direction]
L = 12*(S-2.5)....(i)
Speed of 2nd cyclist = 18 km/hr = 18*5/18 = 5 m/s
Relative speed= S-5
Time to overtake him = 18 s
L = 18*(S-5).....(ii)
(i) == (ii) [Since L or distance is same]
12*(S-2.5) = 18*(S-5)
2*(S - 2.5) = 3*(S-5)
2S - 5 = 3S - 15
S = 10 m/s = 10*18/5 = 36 km/hr
Sub 'S' value in any equation
(ii)== L = 18*(10 m/s - 5 m/s) = 18*5 = 90 m

Hence Length of train = 90 m  && Speed of train = 36 km/hr.
Option (d)
Hope it helps.  

Answer 2

Answer:

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