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51. A train of length 150 metres, takes 10 seconds to pass another train 100 metres long coming from the opposite direction. If the speed of the first train is 30 km/hr, the speed of the second train is
  A.  55 km/hr
  B.  65 km/hr
  C.  50 km/hr
  D.  60 km/hr
     
   
View Answer

Let the speed of second train be x km/hr
Then, relative speed = ( 30 + x ) km /hr
∴ Time taken to cover ( 150 + 100 ) metres at ( 30 + x)km/hr = 10 sec
∴
250 / (30 + x)5/18
= 10
⇒
(250 x 18) / (150 + 5x)
= 10
250 x 18 = 10(150 + 5x)
4500 = 1500 + 50x
50x = 4500 − 1500
50x = 3000
x =
3000 / 50
= 60
⇒ x = 60 km/hr

52. A train 300 metres long is running at a speed of 18 km/hr. How many seconds will it take to cross a 200 metres long train running in opposite direction with 12 km/hr speed?
  A.  60 seconds
  B.  50 seconds
  C.  65 seconds
  D.  55 seconds
     
   
View Answer

Relative speed = (18 + 12) km/hr = 30 km/hr =
(
30 x
5 / 18
)
m/sec =
25 / 3
m/sec
Time taken to cover (300 + 200)m at
25 / 3
m/sec =
(500 x 3) / 25
sec = 60sec

53. A train 540 metre in length is running with speed of 72 km/hr. In what time will it pass a 160 metre long tunnel?
  A.  45 seconds
  B.  55 seconds
  C.  35 seconds
  D.  60 seconds
     
   
View Answer

The speed of train = 72 km/hr =
(
72 x
5 / 18
)
m/sec = 20 m/sec
Sum of the lengths of the train and tunnel = (540 + 160) m = 700 m
∴ Time taken to pass the tunnel = Time taken to cover 700 m at 20 m/sec
=
700 / 20
sec = 35 sec

54. A person standing of a platform feels that a train took 21 seconds to pass through the station, which was 88 metres long and it took 9 seconds to pass him. What is the length of the train and its speed?
  A.  Length 56 metres; Speed 26 km/hr
  B.  Length 66 metres; Speed 26.4 km/hr
  C.  Length 76 metres; Speed 36.4 km/hr
  D.  Length 62 metres; Speed 20.4 km/hr
     
   
View Answer

The length of the train =
88 x 9 / 11 − 9
= 66 m
Speed of the train =
88 / 21 − 9
x
18 / 5
=
132 / 5
= 26.4 km/hr

55. The speeds of two trains are in the ratio of 2:3. They are moving on the opposite directions on parallel tracks. The first train crosses a telegraph pole in 10 seconds whereas the second train crosses the pole in 10 seconds, whereas the second train crosses the pole in 15 seconds. Find the time taken by the trains to cross each other completely.
  A.  13 seconds
  B.  10 seconds
  C.  15 seconds
  D.  20 seconds
     
   
View Answer
Shortcut:
The speed of two trains are in the raio a : b. They are moving in the opposite directions on parallel tracks. The first train crosses a telegraph pole in 'm' seconds whereas the second train crosses a telegraph pole in 'n' seconds. Time taken by the trains to cross each other completely is in
ma + nb / a + b
seconds.
Here, a = 2, b = 3, m = 10, n = 15
Using these values in the shortcut, we get:
Required time =
10 x 2 + 15 x 3 / 2 + 3

=
20 + 45 / 5
=
65 / 5
= 13
Hence, the trains will cross each other in 13 seconds.

56. A train with sped of 36 km/hr crosses a bridge in 18 seconds. Another train 90 metres shorter crosses the same bridge at 27 km/hr. Find the time taken by the second train to cross the bridge.
  A.  8 seconds
  B.  10 seconds
  C.  12 seconds
  D.  22 seconds
     
   
View Answer

Shortcut:
A train with 'a' km/hr crosses a bridge in 'M' seconds. Another train 'N' metres shorter crosses the same bridge at 'b' km/hr. Time taken by the second train to cross the bridge is M
(
a / b
)
−
(
N / b x 5/18
)
seconds.
Here, a = 36, M = 18, N = 90, b = 27
Using these values in the shortcut, we get:
Required time = 18
(
36 / 27
)
−
(
90 / 27 x 5/18
)

= 6 x 4 −
90 x 18 / 27 x 5

= 24 − 2 x 6
= 24 − 12 = 12
Hence, the required time to cross the bridge is 12 seconds.

57. A train crosses a platform in 60 seconds with speed of 45 km/hr. How much time will it take to cross an electric pole if the length of the platform is 100 metres?
  A.  50 seconds
  B.  60 seconds
  C.  42 seconds
  D.  52 seconds
     
   
View Answer

Distance covered by the train in crossing the platform =
45 x 60 / 3600
km =
3 / 4
km = 750 m
∴ Length of the train = 750 − 100 = 650 metres.
∴ Time taken to cross the pole =
650 / 750/60
=
650 x 60 / 750
= 26 x 2 = 52
Hence, the required time to cross the electric pole is 52 seconds.

58. A train having speed of 90 km/hr crosses a bridge in 36 seconds. Another train 100 metres shorter crosses the same bridge at 45 km/hr. Find the time taken by the second train to cross the bridge.
  A.  60 seconds
  B.  64 seconds
  C.  None of these
  D.  74 seconds
     
   
View Answer

Speed of the first train = 90 km/hr.
Converting km/hr into m/sec
90 x
5 / 18
= 5 x 5 = 25 m/sec
Let the length of the bridge be 'a' metre and that of the train 'b' metre.
As per question:
a + b = 25 x 36 = 900 ................eq1
Again, Speed of the second train = 45 km/hr
Converting km/hr into m/sec
45 x
5 / 18
=
25 / 2
m/sec
∴ Time taken by the second train to cross the bridge =
(a − 100) + b / 25/2
=
(a + b − 100) x 2 / 25

Putting the value of (a + b) from eq1, we get:
=
(900 − 100) x 2 / 25
=
800 x 2 / 25
= 64
Hence, the required time to cross the bridge is 64 sec.

59. A train 150 m long crosses a man walking with speed of 6 km/hr in the opposite direction in 6 seconds. The speed of the train is.
  A.  84 km/hr
  B.  80 km/hr
  C.  74 km/hr
  D.  90 km/hr
     
   
View Answer

In 6 sec, the man walking at the rate of 6 km/hr, covers 10 metres.
So, the train has to moe actually ( 150 − 10) i.e 140 metres in 6 sec to cross the man.
Hence, speed of the train =
140 / 6
m/sec =
(
140 / 3
x
18 / 5
)
km/hr = 84 km/hr

60. Two trains of length 121 metres and 99 metres respectively are running in the same direction, one at speed of 40 km/hr and another at 32 km/hr. In what time will they be completely clear of each other from the moment they meet?
  A.  100 seconds
  B.  80 seconds
  C.  99 seconds
  D.  90 seconds
     
   
View Answer

Relative speed = (40 − 32) km/hr = 8 km/hr = 8 x
5 / 18
=
20 / 9
m/sec
Total length = 121 + 99 = 220m
∴ Required time =
Total length / Relative speed
=
220 / 20
x 9 = 99 sec

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