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 train for Fathehpur leaves for every 2 hrs 30 min from Agra station. An announcement was made that train left 37 mins ago and next train comes at 17:00hrs. At what time was the announcement made ? 

A) 15:07 hrs B) 15:20 hrs
C) 15:05 hrs D) 15:00 hrs
 
Answer & Explanation Answer: A) 15:07 hrs

Explanation:

Next train comes at 17:00 hrs.
So, last train will be = 17:00hrs - 2:30hrs
= 14:30hrs
Announcement made after 37 min of the last train.
S0, 14:30hrs + 00:37 min
= 15:07 hrs.

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10 8886
Q:

A jogger is running at 9 kmph alongside a railway track is 240 meters ahead of the engine of a 120 meters long train running at 45 kmph in the same direction. In how much time will the train  pass the jogger ?

A) 48 sec B) 36 sec
C) 18 sec D) 72 sec
 
Answer & Explanation Answer: B) 36 sec

Explanation:

Speed of the train relative to jogger = (45-9) km/hr = 36 km/hr =(36*5/18) m/sec  = 10 m/sec

Distance to be covered =(240 + 120)m = 360 m

 Time taken = 360/10 sec = 36 sec

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Q:

Two trains are running at 60 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 seconds. What is the length of the fast train ?

A. 6623 mts

B. 6632 mts

C.6345 mts

D. 6354 mts

A) Option A B) Option B
C) Option C D) Option D
 
Answer & Explanation Answer: A) Option A

Explanation:

As Trains are moving in same direction,

Relative Speed = 60-20 = 40 kmph

--> 40×518=1009 m/sec

 

Length of Train= Speed * Time

 

Length = 1009×6

2003=6623 mts 

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12 8723
Q:

A train travelling with a speed of 60 km/hr catches another train travelling in the same direction and then leaves it 120m behind in 18 seconds. The speed of the second train is

A) 42 kmph B) 72 kmph
C) 36 kmph D) 44 kmph
 
Answer & Explanation Answer: C) 36 kmph

Explanation:

Given speed of the first train = 60 km/hr = 60 x 5/18 = 50/3 m/s

Let the speed of the second train = x m/s

Then, the difference in the speed is given by

503 - x = 12018

=> x = 10 m/s

=> 10 x 18/5 = 36 km/hr

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21 8583
Q:

A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is :

A) 130 B) 360
C) 500 D) 540
 
Answer & Explanation Answer: C) 500

Explanation:

Speed =[ 78 x ( 5/18 ) ] m/sec = 65/3 m/sec.

 

Time = 1 minute = 60 sec.

 

Let the length of the tunnel be x metres.

 

Then, [ (800 + x )/ 60 ]= 65/3

 

3(800 + x) = 3900

 

 x = 500.

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12 8387
Q:

An Engine length 1000 m moving at 10 m/s. A bird is flying from engine to end with 'x' m/s and coming back at '2x' m/s. Take total time of bird travelling as 187.5 s. Find x and 2x in km/hr ?

A) 21.4 and 42.8 B) 25.2 and 50.4
C) 31.4208 and 62.8416 D) 33.12 and 66.24
 
Answer & Explanation Answer: C) 31.4208 and 62.8416

Explanation:

Birds speeds in mtrs/sec is 'x' and '2x' .
While flying from Engine to end, relative speed = (x+10) m/sec
from end to engine, flying speed = (2x - 10) mtr/sec
so
1000/(x+10) + 1000/(2x-10) = 187.5 secs
solving it, we get
so x = 8.728 m/sec and 2x= 17.456 m/sec

x = 31.4208 km/hr and 2x = 62.8416 km/hr.

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11 7933
Q:

How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction ?

A) 58 sec B) 62 sec
C) 60 sec D) 50 sec
 
Answer & Explanation Answer: D) 50 sec

Explanation:

The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.

Relative speed = 72 -36 = 36 kmph = 36 x 5/18 = 10 mps.

Time required = d/s = 500/10 = 50 sec.

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8 7778
Q:

Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y ?

A) 360 m B) 420 m
C) 460 m D) 320 m
 
Answer & Explanation Answer: B) 420 m

Explanation:

Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m

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