Home ≫ Arithmetic Aptitute ≫ Train ≫ Page 2
11. A girl standing in a train which is moving at the rate of 50 km/hr. She observes that it takes 9 sec for goods train of length of 187.5 metres which is travelling in opposite direction to pass her. Find its speed.
  A.  55 km/hr
  B.  25 km/hr
  C.  42 km/hr
  D.  24 km/hr
     
   
View Answer

Shortcut:
Two trains are moving in opposite directions at a km/hr and b km/hr (where a>b), if the faster train crosses a man in the slower train in t seconds, then the length of the faster train is
[
5 / 18
(a + b)t
]

Here, a = 50, b = ?, t = 9
Using these values in the shortcut, we get:
Length of the train =
[
5 / 18
(50 + b)9
]

187.5 =
[
5 / 18
(50 + b)9
]

187.5 x 18 = 45(50 + b)
3375 = 2250 + 45b
45b = 3375 − 2250
45b = 1125
b =
1125 / 45
= 25
Hence, the speed of the train is 25 km/hr.

12. A train having speed of 25 km/hr takes 18 sec to pass a platform. Next it takes 9 sec to pas a boy who is walking at 5 km/hr in the same direction. What is the length of the train and the platform?
  A.  50 metre, 75 metre
  B.  60 metre, 70 metre
  C.  55 metre, 65 metre
  D.  65 metre, 74 metre
     
   
View Answer

Shortcut:
A train running at a km/hr takes t1 seconds to pass a platform. Next it takes t2 seconds to pass a man walking at b km/hr in the same direction, then the length of the train is
[
5 / 18
(a − b)t2
]
metres and that of the platform is
[
5 / 18
(t1 − t2)a + bt2
]

Here, a = 25, b = 5, t1 = 18, t2 = 9
Using these values in the shortcut, we get:
Length of the train =
[
5 / 18
(25 − 5)9
]
=
[
5 / 18
x 20 x 9
]
=
[
5 / 18
x 180
]
= 5 x 10 = 50 m
Hence, the lenth of train is 50 m.
Lenght of platform =
[
5 / 18
(18 − 9)25 + 5 x 9
]

=
[
5 / 18
x (9 x 25 + 45)
]

=
5 / 18
x 270 = 15 x 5 = 75 m
Hence, the length of platform is 75 m.

13. 150 metres long train crosses a platform of length 250 metres in 30 seconds. In what time this train will cross a bridge of 130 metres?
  A.  20 sec
  B.  25 sec
  C.  22 sec
  D.  21 sec
     
   
View Answer

Shortcut:
L metres long train corsses a bridge of length l1 metres in t seconds. Time taken by the train to cross a platform of l2 metres is given by
[
L + l2 / L + l1
]
t seconds.
Here, L = 150, l1 = 250, l2 = 130, t = 30
Using these values in the shortcut, we get:
Required time =
[
150 + 130 / 150 + 250
]
30
=
[
280 / 400
]
30 = 21 sec
Hence, the train will cross the bridge in 21 seconds.

14. A train passes a pole in 15 seconds and passes a platform of length 100 metres in 30 seconds. The length of the train is.
  A.  105 metres
  B.  110 metres
  C.  95 metres
  D.  100 metres
     
   
View Answer

Shortcut:
L metres long train corsses a bridge of length l1 metres in t seconds. Time taken by the train to cross a platform of l2 metres is given by
[
L + l2 / L + l1
]
t seconds.
Here, L = ?, l1 = 100, l2 = 0, t = 30
l2 = 0, because in place of bridge, pole has been given in the question.
Using these values in the shortcut, we get:
15 =
[
L + 0 / L + 100
]
30
15(L+ 100)= 30L
30L − 15L = 1500
15L = 1500
L = 100
Hence, the length of the train is 100 m.

15. Two trains start at the same time from Goa and Mumbai and proceed towards each other at the rate of 80 km and 95 km/hr respectively. When they meet, it is found that one train has travelled 180 km more than the other. Find the distance between Mumbai and Goa.
  A.  1500 km
  B.  2000 km
  C.  2100 km
  D.  2200 km
     
   
View Answer

Shortcut:
Two trains start at the same time from X and Y and proceed towards each other at the rate of a km/hr and b km/hr respectively. When they meet it is found that one train has travelled d km more than the other. Then the distance between X and Y is
[
a + b / a − b
]
d
Here, a = 95, b = 80, d = 180
Using these values in the shortcut, we get:
=
[
95 + 80 / 95 − 80
]
180
[
175 / 15
]
180 = 2100
Hence, the distance is 2100 km.

16. Two stations A and B are 110 km apart. A train starts from A towards B at the rate of 40 km/hr. Two hours later another train starts from B and travels towards A at the rate of 50 km/hr. When will the first train meet to second train?
  A.  7/3 hrs
  B.  3/7 hrs
  C.  5/3 hrs
  D.  6/7 hrs
     
   
View Answer

Shortcut:
Two trains X and Y are D km apart on a straight line. A train starts from X towards Y at a km/hr. t hours later another train starts from Y twoards X and b km/hr. The time after which the train starting from X will meet the train starting from Y is
D + tb / a + b
hours.
Here, D = 110, a = 40, b = 50, t = 2
Using these values in the shortcut, we get:
=
110 + (2 x 50) / 40 + 50

=
110 + 100 / 90
=
210 / 90
=
7 / 3

Hence, the first train will meet to second train in
7 / 3
hours.

17. A train starts from station A at 9 am and travels at 50km/hr towards station B, 210 km away. Another train starts from station B at 11 am and travels at 60 km/hr towards station A. At what time will they meet and at what distance from A?
  A.  27 km/hr
  B.  11 am, 115 km
  C.  12 noon, 150 km
  D.  9 am, 150 km
     
   
View Answer

Shortcut:
Two trains X and Y are D km apart on a straight line. A train starts from X towards Y at a km/hr. t hours later another train starts from Y twoards X and b km/hr. The time after which the train starting from X will meet the train starting from Y is
D + tb / a + b
hours.
Here, D = 210, a = 50, b = 60, t = 2 [11am − 9am]
Using these values in the shortcut, we get:
=
210 + (2 x 60) / 50 + 60

=
210 + 120 / 110
=
330 / 110
= 3
Hence, the first train will meet to second train in (9 + 3) 12 at noon.
Required distance from A = Distance travelled by first train = 3 x 50 = 150 km

18. A train passes by a stationary man standing on the platform in 7 seconds and passes by the platform in 28 seconds. If the length of the platform is 330 metres, what is the length of the train?
  A.  112 metres
  B.  110 metres
  C.  115 metres
  D.  120 metres
     
   
View Answer

Shortcut:
A train passes by a stationary man standing on the platform or a pole in t1 seconds and passes by the platform completely in t2 seconds . If the length of the platform is L metres, then the length of the train is
t1 x L / t2 − t1
metres and the speed of the train is
L / t2 − t1
m/sec.
Here, t1 = 7, t2 = 28, L = 330
Using these values in the shortcut, we get:
=
7 x 330 / 28 − 7

=
7 x 330 / 21
= 110
Hence, the length of the train is 110 metres.

19. Two stations A and B are 110 km apart. A train starts from A towards B at the rate of 40 km/hr. two hours earlier another train started from B and travels towards A at the rate of 50 km/hr. When will the first train meet to second train?
  A.  3/20 minutes
  B.  25/3 minutes
  C.  5/20 minutes
  D.  20/3 minutes
     
   
View Answer

Shortcut:
Two stations X and Y are D km apart on a straight line. A train starts from X and travels towards Y at a km/hr. Another train, starting from Y, 't' hours earlier, travels towards X at b km/hr. The time after which the train starting from X will meet the train starting from Y is
D − tb / a + b
hours
Here, D = 110, a = 40, b = 50, t = 2
Using these values in the shortcut, we get:
=
110 − (2 x 50) / 40 + 50

=
110 − 100 / 90
=
10 / 9
hours or
20 / 3
minutes
Hence, the first train will meet to second train after
20 / 3
minutes.

20. Two trains of the same length but with different speeds pass a static pole in 4 seconds and 5 seconds respectively. In what time will they cross each other when they are moving in the same direction?
  A.  45 sec
  B.  40 sec
  C.  50 sec
  D.  42 sec
     
   
View Answer

Shortcut:
Two trains of the same length but with different speeds pass a static pole in t1 seconds and t2 seconds respectively. They are moving in the same direction. The time they will take to cross each other is given by
2t1t2 / t2 − t1
seconds.
Here, t1 = 4, t2 = 5
Using these values in the shortcut, we get:
=
2 x 4 x 5 / 5 − 4
= 40 seconds
Hence, the trains will cross each other in 40 seconds.

Copyright © 2020-2022. All rights reserved. Designed, Developed and content provided by Anjula Graphics & Web Desigining .