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64.
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.
Answer & Solution
Answer: (B) 24 sec

Solution:

Answer: Option B

Explanation:

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.

Therefore Required time = ( 500 x 6 ( = 24 sec.
125

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65.
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
Answer & Solution
Answer: (C) 36

Solution:

Let the speed of each train be x m/sec.

Then, relative speed of the two trains = 2x m/sec.

So, 2x = (120 + 120)
12

=> 2x = 20

=> x = 10.

Therefore Speed of each train = 10 m/sec = ( 10 x 18 ( km/hr = 36 km/hr.
5

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66.
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Answer & Solution
Answer: (B) 12

Solution:

Speed of the first train = ( 120 ( m/sec = 12 m/sec.
10

Speed of the second train = ( 120 ( m/sec = 8 m/sec.
15

Relative speed = (12 + 8) = 20 m/sec.

Therefore Required time = [ (120 + 120) ] sec = 12 sec.
20

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67.
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:
Answer & Solution
Answer: (D) 82 km/hr

Solution:

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.

Therefore 220 = 6
( 250 + 5x (
18

=> 250 + 5x = 660

=> x = 82 km/hr.

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68.
A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
Answer & Solution
Answer: (C) 500

Solution:

Speed = ( 78 x 5 ( m/sec = ( 65 ( m/sec.
18 3

Time = 1 minute = 60 seconds.

Let the length of the tunnel be x metres.

Then, ( 800 + x ( = 65
60 3

=> 3(800 + x) = 3900

=> x = 500.

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69.
A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Answer & Solution
Answer: (B) 350 m

Solution:

Speed = ( 300 ( m/sec = 50 m/sec.
18 3

Let the length of the platform be x metres.

Then, ( x + 300 ( = 50
39 3

=> 3(x + 300) = 1950

=> x = 350 m.

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70.
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Answer & Solution
Answer: (B) 150 m

Solution:

Let the length of the train be x metres and its speed by y m/sec.

Then, x = 15     =>     y = x .
y 15

Therefore x + 100 = x
25 15

=> 15(x + 100) = 25x

=> 15x + 1500 = 25x

=> 1500 = 10x

=> x = 150 m.

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