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1. A train crosses a platform in 60 sec at a speed of 45km/hr. How much time will it take to cross an electric pole if the lenght of the platform is 100 meteres?
  A.  8 sec
  B.  60 sec
  C.  52 sec
  D.  40 sec
     
   
View Answer

Distance covered by the train in crossing the platform is
(45 x 60) / 3600
km = 750 metres
So, length of train = (750 − 100) m = 650 metres
Time taken to cross the pole =
(650 x 60) / 750
sec = 52 sec

2. How long does a train 110 metres long running at the rate of 36 km/hr take to cross a bridge 132 metres in length?
  A.  5 sec
  B.  24.2 sec
  C.  12 sec
  D.  25 sec
     
   
View Answer

In crossing the bridge the train has to travel its own length plus the length of the bridge.
Now, 36 km/hr = 36 x
5 / 18
= 10 m/sec
Distance = 110 + 132 = 242 metres.
Hence, the required time =
242 / 10
= 24.2 sec

3. A train 700 m long is running at the speed of 72 km/hr. If it crosses a tunnel in 1 minute, then the lenght of the tunnel is ?
  A.  700 metres
  B.  600 metres
  C.  450 metres
  D.  500 metres
     
   
View Answer

Let the length of the tunnel = y metres.
Speed of train = 75 x
5 / 18
= 20 m/sec
Time taken by the train to cover (700 + y) m =
700 + y / 20
sec
700 + y / 20
= 60
y = 500
Hence, the length of train = 500 metres.

4. A train 150 metres long crosses a man walking at a speed of 6 km/hr in the opposite direction in 6 seconds. The speed of the train is
  A.  84 km/hr
  B.  64 km/hr
  C.  104 km/hr
  D.  90 km/hr
     
   
View Answer

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

5. A train of length 150 metres, takes 10 seconds to pass over another train of 100 metres long coming from the opposite direction. if the speed of the first train be 30 km/hr, the speed of the second train is?
  A.  54 km/hr
  B.  36 km/hr
  C.  60 km/hr
  D.  72 km/hr
     
   
View Answer

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

6. A train 300 metres long is running at a speed of 18 km/hr. How many seconds will it take to cross a 200m long train running in the opposite direction at a speed of 12 km/hr?
  A.  55 sec
  B.  12 sec
  C.  60 sec
  D.  25 sec
     
   
View Answer

Relative speed = (18 + 12) km/hr = 30 km/hr
Converting km/hr into m/sec
30 x
5 / 18
=
25 / 3
m/sec
Time taken to cover (300 + 200)m at
25 / 3
m/sec
=
500 x 3 / 25
sec = 60
Hence, the time taken to cross the train is 60 sec.

7. Two trains are running in opposite directions with the same speed. If the length of each train is 135 metres and they cross each other in 18 seconds, the speed of each train is
  A.  27 km/hr
  B.  105 km/hr
  C.  15 km/hr
  D.  47 km/hr
     
   
View Answer

Let the speed of each train be y m/sec
Then,
135 + 135 / y + y
= 18
or,
270 / 2y
= 18
or, 18 x 2y = 270
36y = 270
y=
270 / 36
=
15 / 2
m/sec
Converting m/sec into km/hr
15 / 2
x
18 / 5
= 27 km/hr
Hence, the speed of the train is 27km/hr.

8. A train 100 metres long meets a man going in opposite direction at 5 km/hr and passes him in 36/5 seconds. At what rate is the train going?
  A.  50 km/hr
  B.  45 km/hr
  C.  36 km/hr
  D.  62 km/hr
     
   
View Answer
Let the speed of train be y m/sec
Speed of man = 5 x
5 / 18
=
25 / 18
m/sec
Relative speed = y +
25 / 18
m/sec =
18y + 25 / 18
m/sec
100 / (18y + 25)/18
=
36 / 5

100 x 18 / (18y + 25)
=
36 / 5

1800 x 5 = 36(18y + 25)
9000 = 648y + 900
648 y = 9000 − 900
y =
8100 / 648
=
225 / 18
m/sec
Converting m/sec into km/hr
y =
225 / 18
x
18 / 5
km/hr
y = 45 km/hr
Hence, the speed of the train is 45 km/hr.

9. Two trains of length 110 metres and 90 metres are running on parallel lines in the same direction with a speed of 35 km/hr and 40 km per hour respectively. In what time will they pass each other?
  A.  100 sec
  B.  160 sec
  C.  130 sec
  D.  144 sec
     
   
View Answer

Relative speed = (40 − 35) km/hr =
25 / 18
m/sec
Time taken by the trains in passing each other = Time taken to cover (110 + 90) m at
25 / 18
m/sec
=
200 x 18 / 25
m/sec = 144
Hence, the train will take 144 sec to pass each other.

10. A train running at 25 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the opposite direction. Find the length of the train and that of the platform.
  A.  100 metres, 25 metres
  B.  120 metres, 50 metres
  C.  80 metres, 55 metres
  D.  110 metres, 95 metres
     
   
View Answer

Speed of the train relative to man = 25 + 5 = 30 km/hr
Converting km/hr into m/sec
30 x
5 / 18
=
25 / 3
m/sec
Distance travelled in 12 seconds at this speed =
25 / 3
x 12 = 100 m
The length of the train = 100 m
Speed of train = 25 km/hr = 25 x
5 / 18
=
125 / 18
m/sec
Distance travelled in 18 sec at this speed =
125 / 18
x 18 = 125 m
Hence, length of the train + length of platform = 125 m
Length of train = 125 − 25 = 100 m
Length of platform = 125 − 100 = 25 m

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