Problems on Trains
Problems on Trains - Important Points
| 6. | A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is: |
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A. 400 m
B. 450 m
C. 560 m
D. 600 m
View Answer Discuss Work SpaceAnswer: option a
Explanation:
Let the length of the first train be x metres.
Then, the length of the second train is (x/2) metres
Relative speed = (48 + 42) kmph
= ( 90 x 5/18 ) m/sec
= 25 m/sec.
Therefore, Time = Length of two trains / Relative speed
=> 12 = [ x + x/2)] / 25
=> 12 = [3x / 2] / 25
=> 3x/2 = 300
=> x = 200
Therefore Length of first train = x = 200 m.
Let the length of platform be y metres.
Speed of the first train = ( 48 x 5/18 ) m/sec
= 40/3 m/sec
Given, the first train passes a railway platform in 45 seconds.
Therefore, Time = (Length of the first train + Length of the platform) / speed of the first train
=> [(200 + y) x 3] / 40 = 45
=> 600 + 3y = 1800
=> y = 400 m
So,length of platform = y = 400 m
| 7. | A train overtakes two persons who are walking in the same direction of the train at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is: |
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A. 45 m
B. 50 m
C. 54 m
D. 72 m
View Answer Discuss Work SpaceAnswer: option b
Explanation:
=> To convert km/hr to m/sec multiply speed with (5 / 18)
2 kmph = ( 2 x 5/18 ) m/sec = 5/9 m/sec
4 kmph = ( 4 x 5/18 ) m/sec = 10/9 m/sec
Let the length of the train be x metres and its speed by y m/sec.
Then, ( x / y - 5/9 ) = 9 and ( x / y - 10/9 ) = 10
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
Therefore Length of the train is 50 m.
| 8. | 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? |
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A. 23 m
B. 23 (2/9) m
C. 27 (7/9) m
D. 29 m
View Answer Discuss Work SpaceAnswer: option c
Explanation:
Relative speed = (40 - 20) km/hr = ( 20 x 5/18 ) m/sec = (50/9) m/sec
Therefore, Length of faster train = ( 50/9 x 5) m = 250/9 m = 27 (7/9 ) m.
| 9. | A train 108 m long moving at the speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is: |
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A. 48 km/hr
B. 54 km/hr
C. 66 km/hr
D. 82 km/hr
View Answer Discuss Work SpaceAnswer: option d
Explanation:
Let the speed of the second train be x km/hr.
Relative speed = (x + 50) km/hr
= [( x + 50 ) x 5/18 ] m/sec
= [ 250 + 5x / 18 ] m/sec.
Distance covered = (108 + 112) = 220 m.
220/ ( 250 + 5x /18 ) = 6
=> 250 + 5x = 660 => x = 82 km/hr.
| 10. | 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? |
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A. 10
B. 12
C. 15
D. 20
View Answer Discuss Work SpaceAnswer: option b
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) = 20 m/sec.
Required time = [( 120 + 120/ 20)] sec = 12 sec.
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