Monday, 4 April 2016

Aptitude Questions - Problems on Trains

Problems on Trains 

The questions based on trains are solved in the same manner as the problems of time and distance are solved but here the length of train is taken into consideration.
1.    The distance travelled by a train to pass a pole or a standing man or tree or any other object of negligible length is equal to the length of the train
     e.g. The distance covered by 150 m long train in a passing a tree =  150m
2.    The distance travelled by a train to pass a platform or another train or bridge or railway station  or any other object having some considerable length is equal to the sum of the lengths of train and the length of the that particular object ( another train or platform or bridge)
e.g. The distance travelled by a 250m long train to cross a bridge of length 150m = Sum of the lengths of train and bridge = 250 + 150 = 400 m
3.    Time taken by a train to cross an object of negligible length =
Length of the train / Speed of the train
4.    Time taken by a train to cross an object of considerable length=
(Length of the train + Length of another train / Speed of the train
5.    If two trains with speeds x kmph and y kmph ( where x>) are moving in same direction, then their relative speed = (x-y)
e.g If two trains with speeds 30 kmph and 40 kmph are running in same direction, then their relative speed = 40-30= 10 kmph
6.    If two trains with speeds x kmph and y kmph are moving in opposite direction, then their relative speed = (x+y) kmph
e.g  if two trains with speeds 30 kmph and 40 kmph are running in opposite direction, then their relative speed = 30 +40 = 70 kmph

Problems on Trains – Solved Problems
1.    A train is running at 48 kmph. If it crosses a pole in 35 seconds, then its length is
      a)   450m              b)500 m         c)525m        d)560m
Answer:C
Explanation: The speed of train = 54 kmph but time given in seconds
We need to convert the speed into m/s => 54 x
5 / 18
=15 m/s
 Time taken = 35 seconds.
Therefore, length of the train= Distance travelled by the train to cross a pole
    = Speed x Time = 15 x 35 = 525 m

2. A 560m long train crosses a standing man in 80 seconds. What is the speed of the train?
a)4 m/s         b)5 m/s         c)6 m/s       d)7 m/s
Answer: D
Explanation: Distance covered by the train is length of the train ( since it is crossing a standing man whose length is negligible)
Distance covered = 560m  Time taken = 80 s
Therefore, Speed of the train=
Distance Covered / Time Taken
=
560 / 80
= 7 m/s

3. The speed of two trains are in the ratio 7:9. If the second train runs 405 km in 5 hours, then the speed of the first train is
     a)   63 kmph         b)72 kmph    c)81 kmph     d)90 kmph
Answer:A
Explanation:
Speed of the second train =
Distance / Time
=
405 / 5
= 81 kmph
Let the speeds of trains be 7x and 9x kmph respectively.
     Speed of 2nd train =9x= 81 kmph => x = 9 kmph
Speed of the first train= 7x = 7 x 9 kmph = 63 kmph.

4. A train 360 m long passes a man walking along the line in opposite direction at the rate of 6 kmph in 18 seconds. Find the speed of the train?
a)   60 kmph  b)66 kmph    c)72 kmph     d)75 kmph
Answer: B
Explanation: Let the speed of the train be x kmph
        Speed of man= 6 kmph
Distance travelled = Length of the train = 360m
As both are moving in opposite direction, the relative velocity= (x+6) kmph
 As distance in meters and time is in seconds. Converting (x+6) kmph into m/s
    Distance = Speed x Time  =>  360 = (x+6)x
5 / 18
x18 
=>   X= 72-6= 66 kmph

5. The time taken by a train running at the speed of 45 kmph of length 270m to cross a stationary train of length 280 m , is
     a)   24 seconds    b)30 seconds   c)36 seconds  d)48 seconds
Answer :C
Explanation: Speed of the train = 45 kmph = 45 x
5 / 18
m/s
Total distance= Length of the moving train + Length of the stationary train=270+280= 450 m
   Time taken = Total distance to be travelled/ Speed of the train =
450 / 45
x
18 / 5
= 36 seconds

6. Two trains of lengths 60m and 80m are moving in opposite directions at speeds of 9 m/s and 5 m/s . The time taken to cross each other is
a)10 seconds   b)8 second  c)6 seconds  d)15 seconds
Answer:A
Explanation: Distance to be travelled= Sum of the lenths of the two trains= 60m +80m = 140m
Two trains are moving in opposite direction, their relative velocity = 9+5 = 14 m/s
Time taken to cross each other =
Distance / Speed
=
140 / 14
= 10 seconds.

7.    Two trains 105m and 135m ong are running towards each other on parallel lines at a speed of 36 kmph and 44 kmph respectively. To cross each other after they meet, it will take
       a)   8 seconds    b)9 seconds  c)10.8 seconds     d)15 seconds
Answer:C
Explanation: Distance covered= Sum of the lengths of two trains= 105+135= 240 m.
  They are moving in opposite direction, relative speed= sum of their speeds = 36+44= 80 kmph
But speed in kmph and distance is in meters. We convert the speed into m/s.= 80 kmph x
5 / 18
Time taken =
Distance / Speed
=
240 / 80
  x
18 / 5
=10.8 seconds

8.    A 240m long train crosses a bridge of thrice its length in 4 minutes. Find the speed of the train?
      a)   3 seconds      b)4 seconds  c)5 seconds  d)6 seconds
Answer: B
Explanation: Length of the train is 240m
So length of the platform = 3 x 240 = 720 m
Time taken to cross bridge= 4 minutes = 240 seconds
Total distance travelled= 
Length of the train + Length of the platform=240+720= 960m.
 Speed of the train =Distance Covered/Time Taken =
960 / 240
= 4 seconds

9. A train crossed a platform in 48 seconds. The train is  running at a speed of 10 m/s What is the length of the platform, if the length of the train is 320m?
a)160m          b)220m          c)250m          d)280m
Answer:A
Explanation: Let length of the platform be x meters
Length of the train = 320m
Time taken to cross platform= 48 seconds
Distance covered by the train to cross platform= Length of the train + length of the platform =(320+x) meters.
Time=
Distance / Speed
=> 48 seconds =
(320+x) / 10
=>x = 480-320=160 meters

10. A 460m long train moving with an average speed of 54 kmph crosses a platform in 12 seconds. A man crosses the same platform in 40 seconds. What is the speed of the man?
a)   5 m/s     b)6 m/s     c)7 m/s       d)8m/s
Answer:B
Explanation: Let the length of the platform be x meters
Given length of the train is 460m
Distance covered by train to cross platform= Sum of the lengths of train and platform
   = (460+x) meters
Time taken to cross platform= 12s
Speed of the train = 54 kmph = 54 x
5 / 18
= 15 m/s
  Speed=
Distance / Time
  => 45=> =
(460+x) / 12
=>x=280
Length of the platform= 280m
Time taken by man to cross the platform= 40 seconds
Therefore Speed of man =
Lenght of platform / Time taken to cross platform
=
280 / 40
= 7  m/s

11. A train travelling with a speed of 80 kmph catches another train travelling in the same direction and then leaves it 150 meters behind in 12 seconds. What is the speed of the second train?
a)25 kmph    b)30 kmph    c)35 kmph     d)40 kmph
Answer:C
Explanation: Speed of first train= 80 kmph
 Let speed of 2nd train be x.
Both are moving in same direction, so their relative speed= 80+x
Speed =
Distance / Time
=>(80-x)=
150 / 12
x
18 / 5
=(80-x)=45=>x=35
 Speed of the 2nd train= 35 kmph.

12. Train A crosses a stationary train in 50 seconds and a pole in 30 seconds with the same speed, The length of the train A is 300m. Find the length of another train?
a)200 meters  b)250 meters  c)350 meters   d)400 meters
Answer:A
Explanation: Length of the first train is 300m
Let length of the 2nd train be x meters.
Distance travelled to cross a pole = Length of the train A = 300 m
Distance travelled to cross stationary train = (Length of the train A + Length of the stationary train) = (300+x)
Speed in both cases is same
=>
Distance to cross stationary train / Time taken to cross the pole
=
Distance to cross the pole / Time talke to cross the pole
=>
(300+x) / 50
=
300 / 30
=> x=200 meters
Length of the stationary train= 200 meters

13. The average speed of a train including stoppages was 36 kmph and excluding stoppages was 45 kmph . How many minutes per hour did the train stop?
a)6 minutes  b)8 minutes  c)10 minutes d)12 minutes
Answer:D
Explanation:
The train travels 36 km per hour including stoppages and 45 km per hour excluding stoppages.
Because of the stops, the train runs (45 -36) = 9 km less per hour
Number of minutes did the train stop =
Decrease in Distance / Original Distance
x 60 minutes
  =
9 / 45
x 60 = 12 minutes.

14. The distance between two stations is 540 km. A train starts from the first station towards the 2nd station at 50 kmph and at the same time another train starts from the 2nd station towards the first station at 40 kmph. Where will they meet from the 2nd station?
a) 300 km      b)240 km       c)150 km       d)275 km
Answer: B
Explanation:
Two trains are moving in opposite direction=> Their relative speed= Sum of their speeds = 40 +50 = 90 kmph
Time to travel the distance of 540 km =>
Distance / Relative Speed
=>
540 / 90
= 6 hours
The train which starts from 2nd station must travel (6x40) = 240 km to meet the another train coming in opposite direction

15. The distance between 2 stations A and B is 330 km. A train starts from A at a speed of 50 kmph at 7 a.m towards B. Another train starts from B towards A at 8 p.m at a speed of 20 kmph. At what time will they meet each other?
a)10 a.m        B)12 P.M   c)1.30 pm     d)2.15 pm
Answer : B
Explanation: Distance = 330 km
   A Train starts from A at a speed of 50 kmph at 7 a.m.
Another Train starts from B at a speed of 20 kmph at 8.a.m
From 7 a.m. to 8 a.m.( in hour), distance travelled by train starts from A = 50 km
       Remaining distance= 330-50= 280 km
        Relative speed of two trains = 50 + 20 = 70 kmph
Time taken to travel 280 km=
Distance / Speed
=
280 / 70
= 4 hours
 After 4 hours from when the 2nd train starts, they will meet each other.

 Time they meet each other = 8 a.m. + 4 hours =12 p.m