Formulas and Quick Tricks for Train Problems
- Time taken by a train x metres long in passing a signal post or a pole or a standing man is equal to the time taken by the train to cover x metres.
- Time taken by a train x metres long in passing a stationary object of length y metres is equal to the time taken by the train to cover x+y metres.
- Suppose two trains are moving in the same direction at u kmph and v kmph such that u>v, then their relative speed = u-v kmph.
- If two trains of length x km and y km are moving in the same direction at u kmph and v kmph, where u>v, then time taken by the faster train to cross the slower train = (x+y)/(u-v) hours.
- Suppose two trains are moving in opposite directions at u kmph and v kmph. Then, their relative speed = (u+v) kmph.
- If two trains of length x km and y km are moving in the opposite directions at u kmph and v kmph, then time taken by the trains to cross each other = (x+y)/(u+v) hours.
- If two trains start at the same time from two points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively, then A's speed : B's speed = (√b : √a)
Questions and Solved Examples on Train Problems
Q.1: A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
A. 69 secs
B. 79 secs
C. 89 secs
D. 99 secs
Answer: C. 89 secs
Explanation: Speed = (240/24) m/sec = 10 m/sec
Therefore, required time = (240 + 650)/10 sec = 89 secs
Q.2: A train running at certain speed crosses a stationary engine in 20 seconds. To find out the speed of the train. Which of the following information is necessary:
A. Only the length of the train
B. Only the length of the engine
C. Either the length of the train and the length of the engine
D. Both the length of the train and the length of the engine
Answer: D. Both the length of the train and the length of the engine
Explanation: Since the sum of the lengths of the train and the length of the engine is needed, So both the lengths must be known.
Train Problems – Basic Concepts, Formulas, Math Tricks, Quantitative Aptitude Questions and Solutions
Q.3: A train moves with the speed of 180 km.hr then its speed in meters per second is:
A. 20 m/sec
B. 30 m/sec
C. 40 m/sec
D. 50 m/sec
Answer: D. 50 m/sec
Explanation: 180 km/hr = (180 × 5/18)m/sec = 50 m/sec
Q.4: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
A. 12 secs
B. 18 secs
C. 36 secs
D. 72 secs
Answer: C. 36 secs
Explanation: Speed of train relative to jogger = 45 – 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec
Distance to be covered = 240 + 120 = 360 m
Time taken = 360/10 = 36 secs
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Q.5: 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:
A. 1 : 3
B. 3 : 2
C. 3 : 4
D. None of these
Answer: B. 3 : 2
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27 x meters and length of the second train = 17 y meters.
(27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y
=> 4 x = 6 y
=> x/y = 3/2
Q.6: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
A. 225 m
B. 235 m
C. 245 m
D. 255 m
Answer: C. 245 m
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec.
Let the length of bridge be x meters.
Then, (130 + X)/30 = 25/2
=> 2(130 + X) = 750
=> X = 245 m
Q.7: A train 100 m long crosses a platform 125 m long in 15 sec. Find the speed of the train?
A. 45 kmph
B. 50 kmph
C. 54 kmph
D. 60 kmph
Answer: C. 54 kmph
Explanation: D = 100 + 125 = 225
T = 15
S = 225/15 * 18/5 = 54 kmph
Q.8: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
A. 20/7 secs
B. 57/7 secs
C. 60/7 secs
D. 80/7 secs
Answer: D. 80/7 secs
Explanation: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps
The time required = d/s = (100 + 100 + 200)/35
=>400/35 = 80/7 secs
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Q.9: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A. 120 metres
B. 150 metres
C. 180 metres
D. 210 metres
Answer: B. 150 metres
Explanation: Speed=(60 * 5/18) = (50/3)
Length of the train = (Speed * Time) = (50/3 * 9) = 150 metres
Q.10: A train sets off at 2:00 pm at the speed of 70 kmph. Another train starts at 3:30 pm in the same direction at the rate of 85 kmph. At what time the trains will meet?
A. 8:30 pm
B. 9:30 pm
C. 10:30 pm
D. 10:45 pm
Answer: C. 10:30 pm
Explanation: D = 70 * 1 1/2 = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3:30 + 7 h = 10:30 pm