Train

23. 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?

by
[A]. 66 km/hr
[B]. 72 km/hr
[C]. 78 km/hr
[D]. 81 km/hr
✅ The correct answer is option D.
4.5 km/hr =

4.5 x
5

m/sec =
5
m/sec = 1.25 m/sec, and

18
4

5.4 km/hr =

5.4 x
5

m/sec =
3
m/sec = 1.5 m/sec.

18
2

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 x
18

km/hr = 81 km/hr.

5

24. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

by
[A]. 1 : 3
[B]. 3 : 2
[C]. 3 : 4
[D]. None of these
✅ The correct answer is option B.
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.

27x + 17y
= 23

x+ y

27x + 17y = 23x + 23y
4x = 6y

x
=
3
.

y
2

25. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

by
[A]. 40 sec
[B]. 42 sec
[C]. 45 sec
[D]. 48 sec
✅ The correct answer is option A.
Formula for converting from km/hr to m/s:  
X km/hr =

X x
5

m/s.

18

Therefore, Speed =

45 x
5
m/sec
=
25
m/sec.

18
2

Total distance to be covered = (360 + 140) m = 500 m.

Formula for finding Time =

Distance

Speed

Required time =

500 x 2
sec
= 40 sec.

25

26. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

by
[A]. 5 sec
[B]. 6 sec
[C]. 7 sec
[D]. 10 sec
✅ The correct answer is option B.
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

   =

66 x
5
m/sec

18

   =

55
m/sec.

3

Time taken to pass the man =

110 x
3
sec = 6 sec.

55

29. 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:

by
[A]. 50 m
[B]. 72 m
[C]. 80 m
[D]. 82 m
✅ The correct answer is option A.
Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 – 36) km/hr

   =

10 x
5
m/sec

18

   =

25
m/sec

9

2x
=
25

36
9

2x = 100
x = 50.

30. 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:

by
[A]. 30 km/hr
[B]. 45 km/hr
[C]. 60 km/hr
[D]. 75 km/hr
✅ The correct answer is option C.
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.

(100 + 100)
= 3x

8

24x = 200

x =
25
.

3

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

3

   =

50
x
18
km/hr

3
5

   = 60 km/hr.