Train

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

by
[A]. 2 : 3
[B]. 4 : 3
[C]. 6 : 7
[D]. 9 : 16
✅ The correct answer is option B.
Let us name the trains as A and B. Then,
(A’s speed) : (B’s speed) = b : a = 16 : 9 = 4 : 3.

12. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

by
[A]. 12 sec
[B]. 24 sec
[C]. 48 sec
[D]. 60 sec
✅ The correct answer is option B.
Relative speed =
= (45 + 30) km/hr

=

75 x
5

m/sec

18

=

125

m/sec.

6

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

Therefore, Distance covered = 500 m.

Required time =

500 x
6

= 24 sec.

125

13. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

by
[A]. 48 km/hr
[B]. 54 km/hr
[C]. 66 km/hr
[D]. 82 km/hr
✅ The correct answer is option D.
Let the speed of the second train be x km/hr.

Relative speed
= (x + 50) km/hr

=

(x + 50) x
5

m/sec

18

=

250 + 5x

m/sec.

18

Distance covered = (108 + 112) = 220 m.

220
= 6

250 + 5x

18

250 + 5x = 660
x = 82 km/hr.

14. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

by
[A]. 69.5 km/hr
[B]. 70 km/hr
[C]. 79 km/hr
[D]. 79.2 km/hr
✅ The correct answer is option D.
Let the length of the train be x metres and its speed by y m/sec.

Then,
x
= 8         x = 8y

y

Now,
x + 264
= y

20

8y + 264 = 20y
y = 22.

Speed = 22 m/sec =

22 x
18

km/hr = 79.2 km/hr.

5

15. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

by
[A]. 45 km/hr
[B]. 50 km/hr
[C]. 54 km/hr
[D]. 55 km/hr
✅ The correct answer is option B.
Speed of the train relative to man =

125
m/sec

10

   =

25
m/sec.

2

   =

25
x
18
km/hr

2
5

   = 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr.
x – 5 = 45         x = 50 km/hr.

16. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

by
[A]. 9 a.m.
[B]. 10 a.m.
[C]. 10.30 a.m.
[D]. 11 a.m.
✅ The correct answer is option B.
Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x – 1) hours = 25(x – 1) km.
20x + 25(x – 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.

17. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

by
[A]. 3.6 sec
[B]. 18 sec
[C]. 36 sec
[D]. 72 sec
✅ The correct answer is option C.
Speed of train relative to jogger = (45 – 9) km/hr = 36 km/hr.

   =

36 x
5
m/sec

18

   = 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.

Time taken =

360
sec
= 36 sec.

10

18. A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

by
[A]. 2.5 min
[B]. 3 min
[C]. 3.2 min
[D]. 3.5 min
✅ The correct answer is option B.
Total distance covered

=

7
+
1

miles

2
4

=
15
miles.

4

Time taken

=

15

hrs

4 x 75

=
1
hrs

20

=

1
x 60

min.

20

= 3 min.

19. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

by
[A]. 9
[B]. 9.6
[C]. 10
[D]. 10.8
✅ The correct answer is option D.
Relative speed = (60 + 40) km/hr =

100 x
5
m/sec
=

250
m/sec.

18
9

Distance covered in crossing each other = (140 + 160) m = 300 m.

Required time =

300 x
9
sec
=
54
sec = 10.8 sec.

250
5

20. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

by
[A]. 120 m
[B]. 240 m
[C]. 300 m
[D]. None of these
✅ The correct answer is option B.
Speed =

54 x
5
m/sec = 15 m/sec.

18

Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.

Then,
x + 300
= 15

36

x + 300 = 540
x = 240 m.