Problems on Trains with Explanation

Q15. Yuvraj is running at 6 km/hr in the opposite direction to that of a train of 110 meters long. A train crosses him in 6 seconds. What is the train's speed?

Answer- Option D

Explanation-

Speed of train relative to Yuvraj =

110 6

m/sec =

280 9

*

18 5

km/hr = 66km/hr

Let the speed of the train be x km/hr. Then, relative speed = (x + 6) km/hr
x + 6 = 66 or x = 60 km/hr

Q16. A passenger is traveling in a train which is moving at 50 km/hr measures that another train, going in opposite direction, takes 9 seconds to cross him. If the length of another train is 280 meters, find its speed?

Answer- Option C

Explanation-

Relative speed

280 9

m/sec =

280 9

x

18 5

km/hr = 112km/hr

Speed of another train = 112 - 50 = 62 km/hr

Q17. A train of length 100 meters is speeding with 30 km/hr. Find the time taken by this train to pass a man standing on the platform?

Answer- Option A

Explanation-

Speed of the train = 30x

5 18

m/sec =

25 3

m/sec

Distance travelled in passing the standing man = 100m
Required time = 100x

3 25

= 12 sec

Q18. A train crosses a bridge in 30 seconds, is moving at 45 km/hr. If its length is 130 meters find the length of the bridge?

Answer- Option D

Explanation-

Speed = 45*

5 18

m/sec =

25 2

, Time = 30sec

Let the length of bridge be x metres.
Then,

130 + x 30

=

25 2

x = 245m

Q19. A train travels a distance of 30 km at a constant speed. If the rate of a train is increased by 5 km per hour, the journey would have taken 2 hours less. Find the original speed of the train?

Answer- Option A

Explanation-

Let x km/hr be the speed of the train.
Time taken to cover 300 km =

300 x

hrs

Time taken to travel 300 km when the speed is increased by 5 km/hr =

300 x + 5

300 x

-

300 x + 5

= 2

x² + 5x - 750 = 0

(x - 25)(x + 30) = 0
x = 25

Q20. In a journey of 600 km, train A takes 3 hours less than a train B. If the rate of train B is 10 km/hr less than that of train A. Find the speed of train B?

Answer- Option C

Explanation-

Let the speed of the train B be x km/hr. Then, speed of the train A is (x + 10) km/hr
Time taken by train B to travel 600 km =

600 x

hrs

Time taken by travel A to travel 600 km =

600 x + 10

600 x

-

600 x + 10

= 3

x² + 10x - 2000 = 0

(x + 50)(x - 40) = 0
x = 40

Q21. A train left 30 minutes later than the Schedule time and to reach its destination in time it increased its speed by 250 km/hr. If the target is 1500 km away, find the speed of the train?

Answer- Option D

Explanation-

Let the speed of the train be x km/hr
Time taken to travel 1500 km =

1500 x

hrs

Time taken to travel 1500 km with the speed of (x + 250) km/hr =

1500 x + 250

1500 x

=

1500 x + 250

+

1 2

x² + 250x - 750000 = 0

(x + 1000)(x - 750) = 0
x = 750