Problems on Trains with Explanation

Q1. If the speed of the train is 72 km/hr, find the time taken by a train of length 100 metres to cross a bridge 132 metres in length.

Answer- Option B

Explanation-

Speed =

72 x 5 18

m/sec = 20 m/sec.

Total distance covered = (100 + 132) m = 232 m/sec.
Required time =

232 20

sec = 11.6 sec.

Q2. A train takes 10 min. to travel a distance of 12 km. If it takes 6 sec. to pass a tower, then find the length of the train?

Answer- Option B

Explanation-

Speed =

12 x 60 10

km/hr = 72 km/hr

Converting into m/sec.

72 x 5 18

m/sec. = 20 m/sec.

Length of the train = (Speed x Time) = (20 x 6) m = 120 m.

Q3. A train is traveling at a speed of 90 km crosses a station in 1 minute. The length of the train and the station are equal. Find the length of the train?

Answer- Option A

Explanation-

Speed =

90 x 5 18

m/sec. = 25 m/sec.

Time = 1 min. = 60 sec.
Let the length of the train and that of the station be x meters.
Then,

2x 60

= 25

x = 750 m

Q4. A train takes 40.5 seconds to cross a platform of length 300 meters. If the train is 150 meters long, find the speed of the train in km/hr?

Answer- Option C

Explanation-

Speed =

150 + 300 40.5

m/sec.

converting in to km/hr

450 x 18 40.5 x 5

km/hr = 40 km/hr

Q5. There are two stations of length 162 meters and 120 meters respectively. A train takes 15 seconds to pass first station and 18 seconds to pass another station. Determine the length of the train?

Answer- Option A

Explanation-

Let the length of the train be x meters.

x + 162 18

=

x + 120 15

15(x + 162) = 18(x + 120)
x = 90 m.

Q6. A train of length 120 meters is moving at 45 km/hr in the same direction as that of the jogger. A jogger is traveling alongside a track is 240 meters ahead of the train's engine. If jogger's speed is 9 km/hr, find the time required by the train to pass the jogger?

Answer- Option D

Explanation-

Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.

36 x 5 18

m/sec. = 10 m/sec.

Distance to be covered = (240 + 120) m = 360 m.
Time taken =

360 10

sec. = 36 sec.

Q7. A faster train of length 0.9 km is moving at 90 km/hr. There is another train of length 1.10 km is moving in opposite direction to that of the faster train at a speed of 60 km/hr. What is the time taken by the slower train to cross the faster train?

Answer- Option C

Explanation-

Relative Speed = (60 + 90) km/hr = 150 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.