Question

11. A train passes a platform 100 m long in 10 seconds and a platform 400 m long in a 25 seconds. Find
the train length
A) 60 m b) 90 m c) 120 m d) 100 m
inning at 5 km/hr in the

Answer 1

Answer:

c) 120 m

Ooooooooooooooooooo

Answer 2

Answer

The length of the train is 100m. So, option d is correct.

Concept

The distance travelled by a body moving at a constant speed is given by

                      d = vt,

where v is the speed of the body,

t is the time taken to cover the distance d.

Given

• The length of the first platform, L₁ = 100m.
• The length of the second platform, L₂ = 400m.
• Time taken by the train to cross the platform 1, t₁ = 10s.
• Time taken to pass the second platform, t₂ = 25s.

Find

The length of the train.

Solution

Distance travelled by the train

If L is the length of the platform, l is the length of the train, then it is clear from the diagram that in crossing the platform the train covers a distance of (L + l) m.

Speed of the train in crossing the first platform

Let the speed of the train in crossing the first platform be v₁ m/s.

Distance covered by the train in crossing the first platform

               L₁ + l = v₁t₁.

Using the given values in the above equation

               v₁ = (100 + l) / 10.                                 ...(1)

Speed of the train in crossing the second platform

Let the speed of the train in crossing the second platform be v₂ m/s.

Distance covered by the train

               (L₂ + l) = v₂t₂.

Using the given values in the above equation

               v₂ = (400 + l) / 25.                              ...(2)

Calculate the length of the train

The train passes both platforms at the same speed so v₁ = v₂. Using equations (1) and (2) then,

     (100 + l) / 10 = (400 + l) / 25

⇒        500 + 5l = 800 + 2l

⇒                   3l = 300

⇒                     l = 100m.

The length of the train is 100m

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