# 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 = $\frac{\left(a+b\right)}{\left(u+v\right)}$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 = $\frac{\left(a+b\right)}{\left(u-v\right)}$sec.

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) = $\left(\sqrt{b}:\sqrt{a}\right)$

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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101 65953
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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132 48578
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 36162
Q:

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is ?

 A) 45 kmph B) 25 kmph C) 30 kmph D) 50 kmph

Answer & Explanation Answer: D) 50 kmph

Explanation:

Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec.
[(25/2) x (18/5)] km/hr = 45 km/hr.
Let the speed of the train be 'S' km/hr.
Then, relative speed = (S - 5) km/hr.
S - 5 = 45 => S = 50 km/hr.

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38 35061
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

$\inline \fn_jvn \therefore$Time taken to pass the man = (100*3/55) = 6 s

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79 33545
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 29055
Q:

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

 A) 230 m B) 240 m C) 260 m D) 270 m

Answer & Explanation Answer: D) 270 m

Explanation:

Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.

Time = 26 sec.

Let the length of the train be x metres.

Then,[ (x+250)/26 ]= 20

=> x + 250 = 520

=> x = 270.

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28 26047
Q:

A train travelling at a speed of 75 mph enters a tunnel $312$miles long. The train is $14$mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

 A) 2.5 min B) 3 min C) 3.2 min D) 3.5 min

Answer & Explanation Answer: B) 3 min

Explanation:

Total distance covered =$72+14$miles =$154$miles

Time taken = $154*75$hrs = $120$ hrs =$120*60min$ = 3 min

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35 26037