Problems on Trains with Solutions
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1. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Ans: 240 m
Speed = (54 * 5/18) m/sec = 15 m/sec
Length of the train = (15 x 20) m = 300 m.
Let the length of the platform be x meters.
then, x+300 / 36 =15
= x+300 = 540
= x = 240m
2. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
So 27x + 17y / x+y = 23
= 27x + 17y = 23x + 23y
= 4x = 6y
= x/y = 3/2
3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Ans: 245 m
Speed = (45* 5/18) m/sec = (25/2) m/sec
Time= 30 Sec
Let the length of bridge be x metres.
Then, 130 + x / 30= 25/2
= 2(130+x) = 750
= x=245 m
4. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Ans: 50 Km/hr
Speed of the train relative to man = (125 / 10) m/sec
= (25 / 2) m/sec
= (25 / 2 * 18 / 5) km/hr
= 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x-5) km/hr
So x – 5 = 45 then x = 50 km/hr.
5. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Ans: 150 meters
Speed= (60 x 5 / 18) m/sec = (50/3) m/sec.
Length of the train = (Speed x Time) = (50 / 3 x 9) m = 150 m.
6. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Ans: 89 Sec
Speed = (240 / 24) m/sec = 10 m/sec.
Required time = (240 + 650 / 10) sec = 89 sec.
7. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 – 36) km/hr
= (10* 5/18) m/sec
= (25/9) m/sec
So, 2x/36 = 25/9
= 2x= 100
= x= 50
8. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Ans: 36 sec
Speed of train relative to jogger = (45 – 9) km/hr = 36 km/hr.
= (36*5/18) m/sec
= 10 m/sec
Distance to be covered = (240 + 120) m = 360 m.
So Time Taken = 360/ 10 sec= 36 sec
9. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Ans: 230 m
Relative speed = (120 + 80) km/hr
= (200 * 5/18) m/sec
= (500 / 9) m/sec
Let the length of the other train be x metres.
then, x+270 / 9= 500/9
= x+270 =500
10. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
Ans: 270 m
Speed= (72*5/18) m/sec = 20 m/sec
Time = 26 sec
Let the length of the train be x metres.
then, x+250/26 = 20
= x+250 =520
11. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
Ans: 60 km/hr
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.
So 100+100/8 = 3x
= 24x= 200
= x= 25/3
So, speed of the faster train = 50/3 m/sec
= (50/3 * 18/5) km/hr
12. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Relative speed = (60 + 40) km/hr = (100*5/18) m/sec = (250/9) m/sec
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = (300*9/250) sec = 54/5 sec = 10.8 sec
13. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Ans: 6 sec
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.
= (66*5/18) m/sec
= (55/3) m/sec
So Time taken to pass the man = (110*3/55) sec = 6 sec
14. A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
Ans: 6 sec
Speed = (78 * 5/18) m/sec = (65/3) m/sec
Time = 1 minute = 60 seconds.
Let the length of the tunnel be x metres.
Then, (800+x/60) = 65/3
= 3 (800+x) = 3900
15. A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Ans: 350 m
Speed = (300/18) m/sec = 50/3 m/sec
Let the length of the platform be x metres.
Then, (x+300/39)= 50/3
= 3 (x+300) = 1950
= x= 350 m
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