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 Problems on Trains Questions

Popular Latest Rated Important Formulae

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 train 150 m long is running with a speed of 68 km/h. In what time will it pass a man who is running at 8 km/ h in the same direction in which the train is going?

A) 8 sec B) 8.5 sec
C) 9 sec D) 9.5 sec
 
Answer & Explanation Answer: C) 9 sec

Explanation:

Relative speed = 68-8 = 60 km/hr = 60 X 5 / 18 m/s = 50/3 m/s

Total distance = 150 m

Time taken to pass a man running in same direction = 150 X 3/50 = 9 seconds

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Q:

Agra and Delhi are 160 km apart. A train leaves Agra for Delhi and at the same time another train leaves Delhi for Agra. Both the trains meet 5 hrs after they start moving. If the train travelling from Agra to Delhi travels 6 km/hr faster than the other train, find the speed of the faster train? 

A) 19 kmph B) 13 kmph
C) 7 kmph D) 9 kmph
 
Answer & Explanation Answer: A) 19 kmph

Explanation:

Let the speed of the slower train = p kmph

ATQ,

Speed of the faster train = (p + 6) kmph

Then,

(p + p + 6) x 5 = 160

10p + 30 = 160

10p = 130

p = 13 kmph

Then, speed of the faster train = p + 6 = 13 + 6 = 19 kmph.

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Q:

A train left from station A for station B at 4 pm at an average speed of 80 kmph. At 8 pm, another train also had left from station A for station B on a parallel track at an average speed of 120 kmph. How far from A is another train expected to overtake the first train?

A) 900km B) 940km
C) 960km D) 980km
 
Answer & Explanation Answer: C) 960km

Explanation:

Ans. 
Distance covered by 1st train in 4 hours = 80*4 = 320 km
Relative speed of 2nd train = 120-80 = 40 km
It will overtake another train in 320/40 = 8 hours
Distance between overtake point and station A = 8*120 = 960 km

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Q:

7 hrs after a goods train passed a station, another train travelling at a speed of 54 km/hr following that goods train passed through that station. If after passing the station the train overtakes the goods train in 11 hours. What is the speed of the goods train?

A) 39.6 km/hr B) 49.5 km/hr
C) 33 km/hr D) 26.4 km/hr
 
Answer & Explanation Answer: C) 33 km/hr

Explanation:
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Q:

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train?
     

A) 42 kmph B) 43 kmph
C) 40 kmph D) 45 kmph
 
Answer & Explanation Answer: C) 40 kmph

Explanation:

We know that,  Speed = Distance/time

 

Let the speed of the train be = x kmph

           NORMAL SPEED                           SPEED 5 KMPH MORE

          Distance = 360 Km                         Distance =360
 
          speed    =  X Kmph                        Speed = (x+5)
 
            Time =360/X                              Time =360/(x+15)
          

 

For the same journey if the speed increased 10 kmph more it will take 1 hour less

 


Time with original speed - time with increased speed = 1

 => (360/x) - (360/x+10) =  1                               

 =>  (360(x+5)-360x)/x(x+5) =1

 =>   360X + 1800 -360X  = X(X+5)

  =>   X^2 + 5x - 1800 = 0

  X = 40 or -45

 X cannot be negetive value
                  

 X = 40 kmph.

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Q:

Train A takes 45 minutes more than train B to travel a distance of 450 km. Due to engine trouble speed of train B falls by a quarter, so it takes 30 minutes more than Train A to complete the same journey. What is the speed of Train A (in km/hr)?

A) 90 B) 120
C) 100 D) 110
 
Answer & Explanation Answer: C) 100

Explanation:
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Q:

A train 500 m long, running at a uniform speed, passes a station in 35 sec. If the length of the platform is 221 m, the speed of the train in km/hr is

A) 721/35 B) 74.16
C) 24.76 D) 78.54
 
Answer & Explanation Answer: B) 74.16

Explanation:
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Q:

Train A takes 1 hour more than train B to travel a distance of 720 km. Due to engine trouble speed of train B falls by a third, so it takes 3 hours more than Train A to complete the same journey? What is the speed of Train A (in km/hr)?

A) 80 B) 90
C) 60 D) 70
 
Answer & Explanation Answer: A) 80

Explanation:
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