Running at a speed of 60 km per hour, a train passed through a 1-5 km long tunnel in two minutes. What is the length of the train ?

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Q: 33 (IAS/2010)
Running at a speed of 60 km per hour, a train passed through a 1-5 km long tunnel in two minutes. What is the length of the train ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,14,8,3,14,5,0

keywords: 

{'long tunnel': [0, 0, 1, 0], 'km': [0, 0, 2, 1], 'minutes': [0, 0, 1, 1], 'length': [0, 0, 1, 0], 'train': [0, 1, 6, 2], 'speed': [0, 1, 2, 0], 'hour': [5, 5, 11, 12]}

We can start by converting the speed of the train from km/h to m/s.

60 km/h = (60 x 1000) / (60 x 60) m/s = 16.67 m/s

We know that the train takes 2 minutes to pass through the tunnel, which is equivalent to 120 seconds.

Let`s assume that the length of the train is `x`.

When the train enters the tunnel, it takes time `t1` to completely enter the tunnel.

Similarly, when the train exits the tunnel, it takes time `t2` to completely exit the tunnel.

The total time taken by the train to pass through the tunnel is t1 + t2.

We can use the formula: distance = speed x time to calculate the distance travelled by the train during t1 and t2.

During t1, the train travels a distance equal to the length of the tunnel + the length of the train.

During t2, the train travels a distance equal to the length of the train.

Therefore, we can write the equation:

1.5 + x = 16.67 x t1 (distance = speed x time)

x = 16.67 x t2 (distance = speed x time)

We know that t1 + t2 = 120 seconds.

Substituting the second equation into the first equation, we get:

1.5 + (16.67 x t2) = 16.67 x (120 - t2)

Solving for t2, we get:

t2 = 30 seconds

Substituting t2 back into the second equation, we get:

x = 16.67 x 30 = 500 meters

Therefore, the length of the train is 500 meters.

Answer: 500 meters.

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