Problems on Trains
- 1. Two trains A and B starts from Howrah and Patna towards Patna and Howrah respectively at the same time. After passing each other, they take 4, h, 48 min and 3 h, 20 min to reach Patna and Howrah, respectively. If the train from Howrah is moving at 45 km/h, then the speed of the other train is?
Options- A. 60 km/h
- B. 45 km/h
- C. 35 km/h
- D. 54 km/h Discuss
Correct Answer: 54 km/h
Explanation:
Given, a = 45 km/h, y = ?, t1 = 4 h 48 min and t2 = 3 h 20 min
Using y = a?t1 / t2= 45?4 h and 48 min /3 h and 20 min
= 45?(24/5h) / (10/3 h) = 45?24 x 3/5 x 10
= 45 x ?1.44 = 45 x 12 = 54 km/h
- 2. A train travelling at 36 kmph completely crosses another train having half its length and travelling in the opposite direction at 54 kmph, in 12 second, If it also passes a railway platform in 1 1/ 2 minutes, the length of the platform is?
Options- A. 560 metres
- B. 620 metres
- C. 700 metres
- D. 750 metres Discuss
Correct Answer: 700 metres
Explanation:
Let the length of slower train be L meters and the
length of faster train be (L/2) meters
Their relative speed = (36 + 54) km/hr
= 90 x (5/18)
= 25 m/sec
? 3L / (2 x 25) = 12
? 3L = 600
? L = 200
? Length of slower train = 200 meters
Let the length of platform by M meters
Then, 200 + M/[36 x (5/18)] = 90 sec.
? 200 + M = 900
? M = 700 meters
Length of platform = 700 meters.
- 3. A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
Options- A. 60
- B. 62
- C. 64
- D. 65 Discuss
Correct Answer: 62
Explanation:
Relative speed =280/9 m / sec = (280/9*18/5) kmph = 112 kmph.
Speed of goods train = (112 - 50) kmph = 62 kmph.
- 4. A train of length 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options- A. 10
- B. 8
- C. 6
- D. 4 Discuss
Correct Answer: 6
- 5. Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 9 hours after they passed each other the ratio of the speeds of the two trains was
Options- A. 2:1
- B. 3:2
- C. 4:3
- D. 5:4 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 3:2
Explanation:
Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)
Therefore, Ratio of the speeds of two trains = = 3 : 2
- 6. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is :
Options- A. 9.5 km/hr
- B. 10 km/hr
- C. 10.5 km/hr
- D. 11 km/hr Also asked in: CAT, Bank PO
Correct Answer: 10 km/hr
Explanation:
Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Therefore, Man's rate against the current = (12.5 - 2.5) = 10 km/hr.
- 7. Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?
Options- A. 48
- B. 24
- C. 38
- D. 36 Discuss
Correct Answer: 24
- 8. Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
Options- A. 42
- B. 36
- C. 28
- D. 20 Discuss
Correct Answer: 36
Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = v. Then relative speed = v + v = 2v
2v = distance/time = 240/12 = 20 m/s
Speed of each train = v = 20/2 = 10 m/s
= 10 × 36/10 km/hr = 36 km/hr
- 9. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?
Options- A. 69.5 km/hr
- B. 70 km/hr
- C. 79 km/hr
- D. 79.2 km/hr Discuss
Correct Answer: 79.2 km/hr
- 10. A train moves with a speed of 108 kmph. Its speed in metres per second is :
Options- A. 10.8
- B. 18
- C. 30
- D. 38.8 Discuss
Correct Answer: 30
Explanation:
108 kmph = 108*[5/18] m/sec = 30 m / s.
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