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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:

Two trains of equal length are running on parallel lines in the same direction at 36 km/hr and 26 km/hr. The faster train passes the slower train in 36 sec. The length of each train is ?

A) 28 mts B) 54 mts
C) 24 mts D) 50 mts
 
Answer & Explanation Answer: D) 50 mts

Explanation:

Let the length of each train be x mts.

Then, distance covered = 2x mts.

Relative speed = 36 - 26 = 10 km/hr.

= 10 x 5/18 = 25/9 m/sec.

2x/36 = 25/9 => x = 50 mts.

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8 9514
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 9469
Q:

A train is traveling at 48 kmph . It crosses another train having half of its length , traveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. What is the length of the platform ?

A) 500 B) 400
C) 360 D) 480
 
Answer & Explanation Answer: B) 400

Explanation:

Speed of train 1 = 48 kmph
Let the length of train 1 = 2x meter

Speed of train 2 = 42 kmph
Length of train 2 = x meter (because it is half of train 1's length)

Distance = 2x + x = 3x
Relative speed= 48+42 = 90 kmph = (90*5/18)  m/s = 25 m/s 


Time = 12 s

Distance/time = speed 

=>3x/12 = 25 (25*12)/3 

Length of the first train = 2x = 200 meter
Time taken to cross the platform= 45 s

Speed of train 1 = 48 kmph = 480/36 = 40/3 m/s

Distance = 200 + y     [where y is the length of the platform] 

x =100m => 200+y = 45* 40/3
y = 400m

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13 9441
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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11 9268
Q:

A train sets off at 3 p.m. at the speed of 70 kmph. Another train starts at 4:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet ?

A) 10:10 pm B) 9:50 pm
C) 11:30 pm D) 10:30 pm
 
Answer & Explanation Answer: C) 11:30 pm

Explanation:

Distance = 70 x 1 ½ = 105 km

Relative Speed = 85 – 70 = 15

Time = 105/15 = 7 hrs

4:30 + 7 hrs = 11.30 p.m.

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14 9204
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 9084
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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7 8949
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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