Problems on Trains
- 1. A train crosses a platform in 30 seconds at a speed of 45km/hr. How much time will it take to cross an electric pole if take to cross an electric pole if the length of the platform is 100 metres?
Options- A. 8 seconds
- B. 30 seconds
- C. 52 seconds
- D. None of these Discuss
Correct Answer: 30 seconds
Explanation:
Distance covered by the train in crossing the platform
= (45 x 30) / 3600
= 3/8 km
= 375 metres
? Length of train = (375 - 100) = 275 meters
? Time taken to cross the pole
= 275 ÷ (375/30)
= (275 x 30) /375
= 30 sec
- 2. A 440 m long train is running at 240 km/h. In what tie will it pass a man running in the direction opposite to that of the train at 24 km/h?
Options- A. 9 s
- B. 6 s
- C. 12 s
- D. 4 s Discuss
Correct Answer: 6 s
Explanation:
Speed of the train relative to man
= (240 + 24) km/h = 264 km/h
= 264 x (5/18) m/s = 220/3 m/s
Distance covered in passing the man = 440 m
? Time taken = (440/220) x 3 = 6 s
- 3. A 280 m long train crosses a platform which is three times of its length, in 6 min 40 s . What is the speed of the train?
Options- A. 3.2 m/s
- B. 1.4 m/s
- C. 2.8 m/s
- D. Cannot be determined Discuss
Correct Answer: 2.8 m/s
Explanation:
Length of the train = 280 m
Length of the platform = 280 x 3 = 840 m
Taken time = 6 min 40 s
= (360 + 40) = 400 s
? Required speed = Distance / Time
= (840 + 280)/400
= 1120/400
= 28 m/s
- 4. Two trains of length 512 m and 528 m are running towards each other on parallel lines at 84 km/h and 60 km/h, respectively. In what time, will they be clear of each other from he moment they meet?
Options- A. 26 s
- B. 25 s
- C. 15 s
- D. 27 s Discuss
Correct Answer: 26 s
Explanation:
Relative speed = (84 + 60) km/h
= 144 km/h = 144 x (5/18) m/s
= 8 x 5 = 40 m/s
Distance covered in passing each other
= 512 + 528 = 1040 m
? Required time = 1040/40 = 26 s
- 5. A train 100 meter in length in length passes a milestone in 10 seconds and another train of the same length travelling in opposite direction in 8 seconds. The speed of the second train is?
Options- A. 36 kmph
- B. 48 kmph
- C. 54 kmph
- D. 60 kmph Discuss
Correct Answer: 54 kmph
Explanation:
Speed of first train = (100/10) = 10 m/sec.
Let the speed of second train be x m/sec
? 200/ 10 + x = 8
? 200 = 80 + 8x
? x = 15
? Speed of second train = 15 m/sec
= (15 x 18/5)
= 54 km/hr.
- 6. Two trains A and B start from station X and Y towards Y and X respectively. After passing each other they take 4 hours 48 minutes ans 3 hour 20 minutes to reach Y and X respectively. If train A is moving at 45 km/hr, then the speed of train B is?
Options- A. 60 km/hr
- B. 54 km/hr
- C. 64.8 km/hr
- D. 37.5 km/hr Discuss
Correct Answer: 54 km/hr
Explanation:
A's speed / B's speed = ?(Time taken by B to reach X) / (Time taken by A to reach Y)
? 45/B's speed = ?(10/3) x (5/24) = 5/6
? B's speed = 45 x (6/5) km/hr = 54 km/hr.
- 7. Two trains Ajanta express and Taj express simultaneously started on two parallel tracks from Meerut to Nagpur, which are 390 km a part. The ratio of the speed of Ajanta express and Taj express is 6 : 7. After how long (in kms) travelling. Taj express exchanges the speed with Ajanta express so that both the trains reach at their destination simultaneously?
Options- A. 150 km
- B. 190 km
- C. 210 km
- D. can't be determined Discuss
Correct Answer: 210 km
Explanation:
Basically they will exchange their speeds just after half of the time required for the whole journey. It means after covering 210 km distance they will exchange their speeds. check it out graphically for more clarification.
- 8. A train P start from Mokama at 5:00 pm reached Hazipur at 6:00 pm. An another train Q starts from Hazipur at 5:00 pm and reaches Mokama at 6:30 pm. At what time, two trains will cross each other?
Options- A. 5 : 36 pm
- B. 4 : 36 pm
- C. 6 : pm
- D. 7 : 00 pm Discuss
Correct Answer: 5 : 36 pm
Explanation:
Let the distance between Mokama and Hazipur be D km
Time taken by train P to cover D km = 1 h
Time taken by Q to cover D km = 3/2 h
? Speed of train P = D km/h
Speed of train Q = 2D/3 km/h .
Let they cross each other T h after 5 : 00 pm.
Then, DT + 2DT/ 3 = D
? T + 2T/3 = 1
? T(1 + 2/3) = 1
? T = 3/5h = (3/5) x 60 = 3 x 12 = 36 min.
Hence, the two trains meet 36 min after 5 : 00 pm.
? Meeting time = 5:36 pm
- 9. The average speed of a train in the onward journey is 25% more than that in the return journey. The train halts for 2 h on reaching the destination. The total time taken to complete to and fro journey is 32 h, covering a distance of 1600 km. Find the speed of the train in the onward journey?
Options- A. 56.25 km/h
- B. 60 km/h
- C. 66.50 km/h
- D. 67 km/h Discuss
Correct Answer: 60 km/h
Explanation:
Let speed in the return journey = V
? Speed in onward journey = (125/100) x V = 5V/4 km/h
Average speed = (2x 5V/4 x V) / (5V/4 + V) = 10V/9 km/h
? 1600 x (9/10V) = 30 [? halts for 2 h ]
? V = 1600 x 9/30 x 10 = 48 km/h
? Speed in onward journey = 5V/4 = 5/4 x 48 = 60 km/h
- 10. A train overtake two persons walking along a railway track. The first one walks at 4.5 km/h and the other one walks at 5.4 km/h. The train needs 8.4 s and 8.5 s respectively , to overtake them. What is the speed of the train, if both the persons are walking in the same direction as the train?
Options- A. 66 kkm/h
- B. 72 km/h
- C. 78 km/h
- D. 81 km/h Discuss
Correct Answer: 81 km/h
Explanation:
Speed of the person = 4 km/h = 4.5 x (5/18) = m/s = 5/4 m/s = 1.25 m/s
Speed of 2nd person = 5.4 km/h = 5.4 x (5/18) m/s = 3/2 m/s = 1.5 m/s
Let speed of train be x m/s.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
? 8.4x - 10.5 = 8.5x - 12.75
? 0.1x = 2.25
? x = 22.5
? Speed of the train = 225 x (18/5 ) = 81 km/h .
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