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Grade 12IIT JEE Entrance Exam

A passenger and a goods train are headed n the same direction on parallel tracks. the passenger train is 240 m long and has a constant velocity of 72kmph. Initially the engine of the passenger train approaches the last wagon of the goods train, t takes 25 s to be in level with the engine of the goods train. if it took 30 s more to completely overtake the goods train, then what is the lenght of the gods train ?

Ananya Moharana

7 Years agoGrade 12

1 Answer

Shubham Sahoo

7 Years ago

Let the length and velocity of goods train to be ‘y’ m and ’x’ m/s respectively.

Now, velocity of passenger train = 72km/h = 72* 5/18 = 20 m/s.

Also, given length of passenger train = 240 m.

Relative velocity of passenger train with respect to goods train = (20 – x) m/s.

Distance covered by passenger train with respect to goods train in 25 s is given by:

y = (20 – x)* 25------(1)

Also, distance covered by passenger train with respect to goods train to overtake it in 30 s is given by :

240 = (20 – x)* 30------(2)

Now, dividing equation (1) by (2) on both the sides simultaneously, we get :

y/240 = 25/30

On solving the above equation we got :

y = 200 m

Hence, the length of goods train is 200 m.

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