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Problems on Trains

- a km/hr = m/s
- a m/s = km/hr
- Time taken by a train of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres.
- Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres.
- Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed = (u – v) m/s.
- Suppose two trains or two bodies are moving in the opposite direction at u m/s and v m/s, then their relative speed is = (u + v) m/s.
- If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other =
- If two trains of length a metres and b metres are moving in same directions at u m/s and v m/s, then time taken by the faster train to cross the slower train =
- If two trains 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) = ()

Ques1. A train moves with a speed of 108 kmph. Its speed in metres per second is:

- 8 b.) 18 c.) 30 d.) 38.8 e.) None of these

Explanation: Answer is C

108 kmph = m/s = 30 m/sec

Ques2. A train 280 m long, running with a speed of 63 km/hr will pass a tree in:

- 15 sec ) 16 sec c.) 18 sec d.) 20 sec e.) None of these

Explanation: Answer is B

Speed = m/sec = m/sec

Time taken = sec = 16 sec

Ques3. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

- 120 metres ) 180 metres c.) 324 metres d.) 150 metres e.) None of these

Explanation: Answer is D

Speed = m/sec = m/sec

Length of the train = (speed * time) = m = 150 m

Ques4. A train covers a distance of 12 km in 10 minutes and if it takes 7 seconds to pass a pole, then the length of the train is:

- 90 m ) 100 m c.) 120 m d.) 140 m e.) None of these

Explanation: Answer is D

Speed = km/hr = m/sec = 20 m/sec

Length of the train = (speed * time) = (20 * 7) m = 140 m

Ques5. The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

- 200 m ) 225 m c.) 235 m d.) 250 m e.) None of these

Explanation: Answer is C

Speed = m/sec = m/sec; Time = 30 sec

Let the length of bridge be x metres.

Then, = ó 2(140 + x) = 750 ó x = 235 m