Time and Distance

1.Nishu is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the speed of the train?
A.35 kmph
B.54 kmph
C.62 kmph
D.70 kmph
E.None of these
Answer – B (54 kmph) 
Explanation – Let the length of the train be x metres.
Then, the train covers x metres in 8 seconds (train is actually covering itself because length of man is very less compartable to train)and (x + 180) metres in 20 seconds.
equate speed in both case,s=d/t
∴ x/8 =( x + 180) / 20 ⇔ 20x = 8(x + 180) ⇔ x = 120.
∴ Length of the train = 120 m.
Speed of the train = [120/8]m/sec (convert to km/hr i.e x 18/5)
=[120/8] x 18/5kmph = 54 kmph.

2.Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
A.27 7/9 m
B.28 m
C.29 m
D.30 2/7 m
E.None of these
Answer – A (27 7/9 m) 
Explanation – When SAME direction- MINUS
Relative speed = (40-20) km/hr = [20 x 5/18] m/sec = [50/9] m/sec.
Length of faster train = sxt=[50/9 x 5] m = 250/9 m = 27 7/9 m.

3.Two train travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. Then length of the faster train is:
A.120 m
B.140 m
C.160 m
D.180 m
E.None of these
Answer – D (180 m) 
Explanation – When OPP. direction-PLUS
Relative speed = (36 + 45) km/hr
= [81 x 5/18] m/sec = [45/2] m/sec.
Length of train = [45/2 x 8] m = 180 m.


4.Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
A.12 sec
B.18 sec
C.14 sec
D.25 sec
E.None of these
Answer – A (12 sec) 
Explanation – Speed of the first train = [120 / 10] m/sec = 12 m/sec.
Speed of the second train = [120 / 15] m/sec = 8 m/sec.
Relative speed = (12 + 8) = m/sec = 20 m/sec.
∴ Required time = (120 + 120) / 20 secc = 12 sec

5.Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
A.12 kmph
B.24 kmph
C.36 kmph
D.48 kmph
E.None of these
Answer – C (36 kmph)
Explanation – Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 ⇔ 2x = 20 ⇔ x = 10.
∴ Speed of each train = 10 m/sec = [10 x 18/5] km/hr = 36 km/hr