Problems on Trains with Explanation

Q8. A man is running at a speed of 3 km/hr in the direction of the train whose length is 50 meters. If the train is moving at a speed of 63 km/hr then how many seconds will this train take to cross the man?

Answer- Option B

Explanation-

Speed of train relative to man = (63 - 3) km/hr = 60 km/hr.

60 x 5 18

m/sec. =

50 3

m/sec.

Time taken to pass the man =

500 x 3 50

sec. = 30 sec.

Q9. Train A 150 meters long is running at the speed of 45 km/hr. There is another train B 200 meters long is moving at 40 km/hr. If both the trains are on parallel tracks and are running in the same direction, then find the time they will take to cross each other?

Answer- Option A

Explanation-

Relative speed = (45 - 40) km/hr = 5 km/hr.

5 x 5 18

m/sec. =

25 18

m/sec.

Total distance covered = Sum of lengths of trains = 350 m.
Time taken =

350 x 18 25

sec. = 252 sec.

Q10. A station 100 meters long is crossed by a train in 60 seconds. If the train's speed is 45 km/hr, find the time it takes to pass an electric pole?

Answer- Option C

Explanation-

Speed =

45 x 5 18

m/sec. =

25 2

m/sec.

Let the length of the train be x meters.
Then,

x + 100 12.5

= 60 or x = 650 m.

Time taken by the train to cross an electric pole =

650 x 2 25

sec. = 52 sec.

Q11. Two trains P and Q are moving in opposite direction at a rate of 36 km/ hr and 45 km/hr respectively. A passenger is sitting in train P, finds that his train passes train Q in 8 seconds. What is the length of train Q?

Answer- Option A

Explanation-

Relative speed = (36 + 45) km/hr = 81 km/hr

81 x 5 18

m/sec. =

45 2

m/sec.

Length of train =

45 x 8 2

m = 180 m.

Q12. Train A passes another train B, traveling in the same direction in 2 minutes. If train A and B are 100 meters and 200 meters long respectively and train A's speed is 120 km/hr what train B's speed is?

Answer- Option D

Explanation-

Let the speed of train B be x km/hr
Speed of A relative to B = (120 - x) km/hr = (120 - x)*

5 18

m/sec =

600 - 5x 18

m/sec
300 = 120

600 - 5x 18

x = 111

Q13. Two bikers are riding in the same direction of a train at a speed of 2 km/hr, and 4 km/hr. A train overtakes them completely in 9 and 10 seconds respectively. What is the length of the train?

Answer- Option B

Explanation-

2 km/hr = 2*

5 18

m/sec =

5 9

m/sec
4 km/hr = 4*

5 18

m/sec =

10 9

m/sec
Let the length of the train be x metres and its speed be y m/sec
Then, x = 9*

y -

5 9

and

x = 10*

y -

10 9

On solving these two equations, we get x = 50
Length of the train = 50 m

Q14. A train P starts from Jaipur at 11 AM and reaches Mathura at 12 PM while another train Q starts from Mathura at 11 AM and reaches Jaipur at 12:30 PM. At what time the two trains will cross each other?

Answer- Option A

Explanation-

Suppose, the distance between Jaipur and Mathura is x km
Time taken by P to cover x km = 1 hour
Time taken by Q to cover x km = 1.5 hours
Speed of P = x km/hr, Speed of Q =

2x 3

km/hr

Let them meet y hours after 11 am. Then
xy +

2xy 3

= x

y =

3 5

hours = 36 min