Problems on Trains Questions

FACTS  AND  FORMULAE  FOR  PROBLEMS  ON  TRAINS

 

 

1. a km/hr = [a x (5/18)] m/s.

 

2. a m/s = [a x (18/5)] km/hr.

 

3. 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.

 

4. Time taken by a train of length 1 metres to pass a stationary object of length b metres is the time taken by the train to cover (1 + b) metres.

 

5. 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 relatives speed = (u - v) m/s.

 

6. Suppose two trains or two bodies are moving in opposite directions at u m/s and v m/s, then their relative speed = (u + v) m/s.

 

7. 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 = (a+b)(u+v)sec.

 

8. If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then the time taken by the faster train to cross the slower train = a+bu-vsec.

 

9. 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

Q:

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.?

A) 60 B) 62
C) 64 D) 65
 
Answer & Explanation Answer: B) 62

Explanation:

Relative speed =280/9  m / sec = (280/9*18/5)  kmph = 112 kmph.

 

Speed of goods train = (112 - 50) kmph = 62 kmph.

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133 48915
Q:

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 :

A) 9.5 km/hr B) 10 km/hr
C) 10.5 km/hr D) 11 km/hr
 
Answer & Explanation Answer: B) 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.

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103 66083
Q:

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?

A) 10 B) 8
C) 6 D) 4
 
Answer & Explanation Answer: C) 6

Explanation:

Distance = 110 m

Relative speed = 60 + 6 = 66 kmph (Since both the train and the man are in moving in opposite direction)

= (66*5/18)  m/sec = 55/3  m/sec

Time taken to pass the man = (100*3/55) = 6 s

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79 33613
Q:

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 

A) 2:1 B) 3:2
C) 4:3 D) 5:4
 
Answer & Explanation Answer: B) 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 = 9:4 = 3 : 2

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75 29322
Q:

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

A) 42 B) 36
C) 28 D) 20
 
Answer & Explanation Answer: B) 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

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72 36295
Q:

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 ?

A) 69.5 km/hr B) 70 km/hr
C) 79 km/hr D) 79.2 km/hr
 
Answer & Explanation Answer: D) 79.2 km/hr

Explanation:

Let the length of the train be x metres and its speed by y m/sec.


Then, x/y = 8 => x = 8y


Now, (x+264)/20 = y
8y + 264 = 20y
y = 22.
Speed = 22 m/sec = (22*18/5) km/hr = 79.2 km/hr.

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57 15874
Q:

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?

A) 48 B) 24
C) 38 D) 36
 
Answer & Explanation Answer: B) 24

Explanation:

Less Cogs  more turns and less time  less turns

 

    Cogs  Time  TurnsA  54       45       80B   32       8          ?

Number of turns required=80 × 54/32 × 8/45  = 24 times

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57 19633
Q:

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

A) 10.8 B) 18
C) 30 D) 38.8
 
Answer & Explanation Answer: C) 30

Explanation:

108 kmph = 108*[5/18] m/sec = 30 m / s.

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