Problems on Trains

1.

A 180m long train is running at 72 Kmph. If it crossed the platform in 20sec. then find the platform Length?

   A.) 210m
   B.) 220m
   C.) 240m
   D.) 250m

Answer: Option 'B'

Length = Speed*Time 
L = 72K.M/H*T 
L=72*5/18*20 
L= 400M. 
Length of Platform= Length-Length of the Train 
Length of Platform= 400-180 
Length of Platform=220m 

2.

A boat is rowed down a river 40 km in 5 hr and up a river 21 km in 7 hr. Find the speed of the boat and the river.

   A.) 61/12 kmph
   B.) 4.5 kmph
   C.) 5 kmph
   D.) 5.5 kmph

Answer: Option 'D'

Speed of the boat downstream = 40/5 = 8 kmph
Speed of the boat upstream = 21/7 = 3 kmph
Speed of the boat = 1/2 ( 8+3) = 11/2 = 5.5 kmph

3.

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

   A.) 96 km/hr
   B.) 81 km/hr
   C.) 51 km/hr
   D.) 76 km/hr

Answer: Option 'B'

4.5 km/hr = ( 4.5 x 5/18 ) m/sec = 5/4 m/sec = 1.25 m/sec, and
5.4 km/hr = ( 5.4 x 5/18 ) m/sec = 3/2 m/sec = 1.5 m/sec.
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Therefore Speed of the train = ( 22.5 x 18/5 ) km/hr = 81 km/hr.

4.

A train is moving at a speed of 132 km/hr .If the length of the train is 110 metres ,how long will it take to cross a railway platform 165 metres long? 

   A.) 7 sec
   B.) 7 1/2 sec
   C.) 5 sec
   D.) 6 1/2 sec

Answer: Option 'B'

7 1/2 sec

5.

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 km/hr
   B.) 50 km/hr
   C.) 54 km/hr
   D.) 55 km/hr

Answer: Option 'B'

Given, Length of the train = 125 meter
Time taken by the train to pass the man = 10 sec
Speed of man =5 km/hr
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 x km/hr.
Since Man and Train are moving in same direction, speeds must be subtracted
Then, relative speed = Speed of train -Speed of man
=> x - 5 = 45
=> x = 50 km/hr

6.

Speed of a goods train is 72 km/hr. This train crosses a 250 meter platform in 26 seconds. Then find the length of goods train.

   A.) 270
   B.) 280
   C.) 260
   D.) 250

Answer: Option 'A'

Speed = 72 kmph = 72 x (5/18) = 20 m/sec
Time = 26 seconds.
Total distance =Length of train + platform = x + 250
Distance = Speed x time => x+ 250 = 20 x 26 = 520 = > x= 270 m

7.

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

   A.) 48 seconds
   B.) 42 seconds
   C.) 40 seconds
   D.) 45 seconds

Answer: Option 'C'

Given, Length of train =360 m
Length of bridge =140 m
Speed of train = 45 km/hr ---> Converting into meter/ second
= 45 × (5/18) m / sec
= 12.5 m/sec
=>Speed of train =12.5 m/sec
Required Time =(Length of train + Length of bridge) /Speed of train
= (360 + 140) / 12.5
= 500 / 12.5
= 40 sec
=>Required Time =40 sec

8.

A train 100 m long is running at the speed of 30 km/hr.Find the time taken by it to pass a man standing near the railway line:

   A.) 12 sec
   B.) 10 sec
   C.) 8 sec
   D.) 5 sec

Answer: Option 'A'

12 sec

9.

A 400m long train is running at 72 Kmph. how much time it will take to cross an electric pole? 

   A.) 15sec
   B.) 20sec
   C.) 19sec
   D.) 21sec

Answer: Option 'B'

Formula: Distance = Speed × Time
If we convert Kmph in to Mpsec multiply by 5/18,
400 = 72 KmpH × time
400 = 72×5/18 × time
Time = 20Sec

10.

Two trains running in opposite directions at 40kmph and 50kmph, cross each other in 30sec. the length of one train is 250m, then find the length of other one? 

   A.) 440m
   B.) 490m
   C.) 500m
   D.) 510m

Answer: Option 'C'

L = S×T 
L = 90×5/18×30 
L = 750m 
Length of second train= total length - Length of first train
= 750 - 250 = 500m

11.

A train is running at 108 Kmph. It was crossed an electronic pole in 28sec. find the length of the train? 

   A.) 480m
   B.) 840m
   C.) 640m
   D.) 740m

Answer: Option 'B'

L = S × T 
L = 108 Kmph × 28Sec 
L =108 × 5/18 × 28 
L= 840m

12.

How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

   A.) 25
   B.) 30
   C.) 40
   D.) 45

Answer: Option 'B'

Given, Length of the train = 500 m
Speed of the man = 3 km/hr
Speed of the train = 63 km/hr
Time taken by the train to cross a man = Length of the train / (speed of the train – speed of the man)
=> Time = 500 m / (63 – 3) km/hr
=> Time = 500 m / 60 km/hr
(to convert 60 km/hr to m/sec)
=> Time = 500 m / [60 × (5/18) m/sec]
=> Time = {500 / [60 × (5/18)]} sec
=> Time = {(500 × 18) / (60 × 5)} sec
=>Time = 30 sec

13.

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? 

   A.) 120 m
   B.) 240 m
   C.) 300 m
   D.) 250 m

Answer: Option 'B'

Given,speed of the train = 54 km/hr
---> converting this speed into meter/ sec
=> Speed of the train = (54 x 5 / 18 ) m/sec = 15 m/sec
Given that, thetrain passesa man in 20 seconds.
=> Length of the train = speed of the train × Time to pass theman 
= 15 × 20
300 meter
Given that, thetrain passesa platform in 36 seconds.
=> Length of the train + Length of the platform = speed of the train × Time to pass the platform
=> 300 +Length of the platform = 15 × 36
=>Length of the platform = 540 - 300
=>Length of the platform = 240 meter.

14.

A train 250m long can cross a bridge of length 350m in 20sec, then find the speed of the train? 

   A.) 30 m/sec
   B.) 32 m/sec
   C.) 35 m/sec
   D.) 36m/sec

Answer: Option 'A'

Length = Speed × Time 
Speed= Length/Time 
Speed= 600/20 
Speed=30 m/sec 

15.

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.) 500
   B.) 540
   C.) 360
   D.) 130

Answer: Option 'A'

Given, Length of the train = 800 m
Speed ofthe train = 78 km/hr
= 78 × (5 / 18) m/s
= 390 / 18 m/s
Time to cross the tunnel = 1 min = 60 sec
Formula: Distance = Speed × Time
=> Length of the train + length of the tunnel = Speed of the train × Time to cross the tunnel
=> 800 + length of the tunnel = (390 / 18) × 60
=> 800 + length of the tunnel = 23400 / 18
=> 800 + length of the tunnel = 1300
=> length of the tunnel = 1300 - 800 = 500 m

16.

A train crosses a platform of 120m in 15sec, same train crosses another platform of length 180m in 18sec. then find the length of the train?

   A.) 175m
   B.) 180m
   C.) 185m
   D.) 170m

Answer: Option 'B'

Length of the train be ‘X’ 
X + 120/15 = X + 180/18 
6X + 720 = 5X + 900 
X = 180m

17.

A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? 

   A.) 230 m
   B.) 240 m
   C.) 260 m
   D.) 320 m

Answer: Option 'A'

Given the length of the first train = 270 metres.
Let the length of the second train be x metres
Relative speed = Speed of first train + Speed of Second Train
= (120 + 80) kmph
= ( 200 x 5/18 ) m/sec
= 1000/ 18 m/sec.
Therefore,Time taken by the first train to cross the another train = Length of two trains / Relative speed
=> 9 = [ 270 + x ] / (1000/ 18)
=> 9 = ([ 270 + x ] * 18) / 1000
=> 9 * 1000 / 18 =270 + x
=> 500 = 270 + x
=> 500 - 270 = x
=> 230 = x
Thus thelength of the second train = 230 metres

18.

A man can row 30 km upstream and 44 km downstream in 10 hrs. It is also known that he can row 40 km upstream and 55 km downstream in 13 hrs.Find the speed of the man in still water

   A.) 8 km/hr
   B.) 6 km/hr
   C.) 12 km/hr
   D.) 4 km/hr

Answer: Option 'A'

Let the speed of the man in still water be x kmph and speed of the stream be y kmph
Downstream speed = x+y kmph and
Upstream Speed = x-y kmph
=>30 / (x-y) + 44 / (x+y) = 10 and
40 / (x-y) + 55 / (x+y) = 13
Let 1/ (x+y) = u and 1/ (x-y) = v
----> 30 u + 44 v = 10 ---> multiply this eqn by 4
----> 40 u + 55 v = 13 ---> multiply this eqn by3
Solving these two linear equation we get u = 1/5 and v = 1/11
----> x - y = 5 and x+y = 11
Solving these two linear equation we get
-----> x = 8 and y = 3
So the speed of the man in still water = x = 8 km/ph

19.

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

   A.) 48 km/hr
   B.) 54 km/hr
   C.) 66 km/hr
   D.) 82 km/hr

Answer: Option 'D'

Let the speed of the second train be x km/hr.
Relative speed = (x + 50) km/hr = [( x + 50 ) x 5/18 ] m/sec = [ 250 + 5x / 18 ] m/sec.
Distance covered = (108 + 112) = 220 m. 220/ ( 250 + 5x /18 ) = 6 => 250 + 5x = 660 => x = 82 km/hr.

20.

Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

   A.) 36
   B.) 45
   C.) 48
   D.) 49

Answer: Option 'C'

Relative speed = (60+ 90) km/hr
= ( 150 x 5/18 ) m/sec
= (125/3 ) m/sec
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time =( 2000 x 3/125) sec = 48 sec.


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