Problems on Trains

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.


1. A 300 meter long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?

A. 150 m

B. 350 m

C. 420 m

D. 600 m


Answer

                  Ans: Option B

       Explanation:

       Length of the train = distance covered in crossing the post

                                     = speed × time

                                     = speed × 18

       Speed of the train = 300/18 m/s = 50/3 m/s

       Time taken to cross the platform = 39 s

       (300+x)/(50/3) = 39 s , where x is the length of the platform

       300+x = (39 × 50) / 3 = 650 meter

       x = 650-300 = 350 meter. 


2. The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:

A.200 m              

B.225 m

C.245 m              

D.250 m


Answer

                  Ans: Option C

       Explanation:

       Speed = (45/18) x5m/sec=25/2m/sec.

       Time = 30 sec.

       Let the length of bridge be x meters.

       Then, (130 + x)/30=25/2

                  2(130 + x) = 750

                  x = 245 m. 


3. Trains A and B start from station P in the same direction at 9:00 am and 10:00 am respectively. If the speeds of the trains are in the ratio 3:4, at what time will train B cross train A?

A. 1 pm

B. 12:30 pm

C. 3 pm

D. 2 pm


Answer

                  Ans: Option A

       Explanation:

Let the speeds of train A be 3x kmph and 4x kmph.

Distance travelled by train A in the first 1 hour (9 am to 10 am) = 3x km.

Relative speed of trains moving in the same direction = 4x-3x = x kmph

Train A is 3x km ahead of B at 10 am.

Time taken to cover 3x km with a relative speed of x kmph = 3x/x = 3 hours

Train B crosses train A at 1 pm.

 


4. Two, trains, one from Kathmandu to Pokhara and the other from Pokhara to Kathmandu, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

A. 2 : 3  

B. 4 : 3

C. 6 : 7   

D. 9 : 16


Answer

                  Ans: Option B

       Explanation:

       Let the name of the trains be A and B. Then,

       (A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3. 

 


5. A train having a length of 270 meter is running at the speed of 120 kmph. It 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. 320 m             

B. 190 m

C. 210 m             

D. 230 m


Answer

                  Ans: Option D

       Explanation:

       Relative speed = 120+80 = 200 kmph = 200×10/36 m/s = 500/9 m/s

       Time = 9s

       Total distance covered = 270 + x where x is the length of other train

         (270+x)/9 = 500/9

       => 270+x = 500

       => x = 500-270 = 230 meter 


6. A train crosses a man standing on a platform in 20 seconds and the platform in 100 seconds. If the train is 300m long, find the length of the platform.

A. 1 km

B. 1.2 km

C. 700 m

D. 900 m


Answer

                  Ans: Option B

       Explanation:

       Let the length of the platform be x m.

       300/20 = (300+x)/100

       15 = (300+x)/100

       1500 = 300+x

        x = 1200m

           = 1.2 km 


7. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

A. 50 m

B. 72 m

C. 80 m

D. 82 m


Answer

                  Ans: Option A

       Explanation:

       Let the length of each train be x meters.

       Then, distance covered = 2x meters.

       Relative speed = (46 – 36) km/hr.

                               =10 x (5/18) m/sec

                               = (25/9) m/sec

         Then, 2x/36 = 25/9

                   2x = 100

                   x = 50. 


8. Two trains of equal length take 12 seconds and 18 seconds respectively to cross a telegraph post. Find the ratio of their speeds.

A. 2:3

B. 3:2

C. 4:3

D. 3:4


Answer

                  Ans: Option B

       Explanation:

       Ratio of their speeds is inversely proportional to the ratio of the time taken

       since the distance travelled (length of the trains) is equal.

       So, Ratio of their speeds = 18:12 = 3:2 


9. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

A. 30 km/hr         

B. 45 km/hr

C. 60 km/hr         

D. 75 km/hr


Answer

                  Ans: Option C

       Explanation:

       Let the speed of the slower train be x m/sec.

       Then, speed of the faster train = 2x m/sec.

       Relative speed = (x + 2x) m/sec = 3x m/sec.

     Then, (100 + 100)/8= 3x

                24x = 200

                x =25/3             

     So, speed of the faster train = 50/3m/sec

                                                  =(50/3)x(18/5)km/hr

                                                  = 60 km/hr. 


10. Stations A and B are 110 km apart. Train C starts from A at 4:00 pm and travels to B at a speed of 40 kmph. Train D starts from B at 4:30 pm and travels towards A at a speed of 50 kmph. They meet at

A. 5:30 pm

B. 5:10 pm

C. 5:15 pm

D. 5:20 pm


Answer

                  Ans: Option A

       Explanation:

Distance travelled by C in ½ an hour (at 4:30 pm) = 40* ½ = 20 km

Let the distance travelled by C after 4:30 pm till it meets D be x km.

Time taken by C to travel x km = Time taken by D to travel 90-x km x/40

= (90-x)/50 x=40 km

Time taken = 1 hour

They meet at 5:30 pm (an hour after 4:30 pm).

 


11. 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. 66 km/hr         

B. 72 km/hr

C. 78 km/hr         

D. 81 km/hr


Answer

                  Ans: Option D

       Explanation:

4.5 km/hr =(4.5 x5)/18m/sec =     5/4m/sec = 1.25 m/sec, and

5.4 km/hr =(5.4 x5)/18m/sec =     3/2m/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

  Speed of the train =(22.5 x18)/5km/hr = 81 km/hr. 


12. Two trains travelling in opposite directions at speeds of 110 kmph and 90 kmph cross each other for 9s. If the length of the first train is 225m, find the length of the second train.

A. 275m

B. 250m

C. 225m

D. 200m


Answer

                  Ans: Option A

       Explanation:

       Relative speed of the trains = 110+90

                                                   = 200 kmph

                                                   = 200*(1000/3600) m/s

                                                   = 500/9 m/s

       Total length of two trains = 500/9 m/s * 9 s

                                               = 500 m

Then, length of 2nd train = 500 – 225 = 275m 


13. 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 m             

B. 360 m

C. 480 m             

D. 400 m


Answer

                  Ans: Option D

       Explanation:

Speed of train1 = 48 kmph

Let the length of train1 = 2x meter

Speed of train2 = 42 kmph

Length of train 2 = x meter (because it is half of train1's length)

Distance = 2x + x = 3x

Relative speed= 48+42 = 90 kmph = 90×10/36 m/s = 25 m/s

Time = 12 s

Distance/time = speed

=> 3x/12 = 25

=> x = 25×12/3

        = 100 meter

Length of the first train = 2x = 200 meter

Time taken to cross the platform= 45 s

Speed of train1 = 48 kmph = 480/36 = 40/3 m/s

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

=> 200 + y = 45×40/3 = 600

=> y = 400 meter 


14. Two trains P and Q are traveling from station A to station B at speeds of 100kmph and 120 kmph respectively. Train Q stops at station C for 10 minutes but reaches station B 5 minutes before train P. Find the distance between stations A and B.

A. 50 km

B. 100 km

C. 120 km

D. 150 km


Answer

                  Ans: Option D

       Explanation:

       Let the distance between A and B be x km.

       Time taken by train P = x/100

       Time taken by train Q = x/120

       x/100 = (x/120) + (1/4) x

                 = 150km 


15. A train, having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train

A. 10 sec             

B. 8 sec

C. 6 sec

D. 4 sec


Answer

                  Ans: Option C

       Explanation:

       Distance = 110 m

       Relative speed

       = 60+6

       = 66 kmph (Since both the train and the man are in moving in opposite direction)

       = 66×10/36 mps = 110/6 mps

       Time = distance/speed = 110/(110/6) = 6 s 


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