Problem on Trains
- The distance between two station A and B is 220 km. A train leaves A toward B at an average speed of 80 km/hr. after half an hour another train leaves B toward A at an average speed at 100 km/hr. the distance of the point of two train meet, from A is ?
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Let the required distance be x km.
Then, ( x/80 ) - ( 220 - x ) / 100 = 1/2Correct Option: A
Let the required distance be x km.
Then, ( x/80 ) - ( 220 - x ) / 100 = 1/2
⇒ 5x - 4( 220 - x ) = 200
⇒ 9x = 1080
⇒ x = 120 km
∴ Required distance = 120 km
- X and Y are two station 500 km apart. A train start from X and moves toward Y at 20 km/hr another train station from Y at the same times and moves toward X at 30 km/hr. How far from X will they cross each other ?
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Suppose they meet x km. from X
Then, x/20 = (500 - x)/30Correct Option: A
Suppose they meet x km. from X
Then, x/20 = (500 - x)/30
⇒ 30x = 10000 - 20x
∴ x = 200 km.
- 150 meter long train takes 10 second two pass a man who is going in same direction at the speed of 2 km/hr . What is the speed of the train ?
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Let the speed of the train be Y km/hr
∴ length of the train = 150 m
= 150/1000 = 3/20 km.
Time taken to cross the man = 10 seconds
= 10/ (60 x 60) = 1/360 hrs .
∵ time = Length of the train /( speed of the train - speed of the man )
∴ 1/360 = ( 3 / 20) / ( Y - 2)Correct Option: B
Let the speed of the train be Y km/hr
∴ length of the train = 150 m
= 150/1000 = 3/20 km.
Time taken to cross the man = 10 seconds
= 10/ (60 x 60) = 1/360 hrs .
∵ time = Length of the train /( speed of the train - speed of the man )
∴ 1/360 = ( 3 / 20) / ( Y - 2)
⇒ (Y - 2 ) = 3/20 x 360
⇒ (Y - 2 )= 54
⇒ Y = 54 + 2
= 56 km/hr.
- A train running at the speed of 45 kmph took 12 seconds in passing a certain point. Then the length of the train must be ?
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∵ Speed = (45 x 5/18) = (25/2) m/sec
Distance = (Time x Speed)Correct Option: C
∵ Speed = (45 x 5/18) = (25/2) m/sec
Distance = (Time x Speed) = (12 x 25 / 2 ) meters
= 150 meters
∴ Length of the train = 150 meters
- A train 75 meters long is running with a speed of 20 km/hr. It will pass a standing man in ?
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∵ Speed of the train = (20 x 5/18) = (50/9) m/sec
Correct Option: B
∵ Speed of the train = 20 x (5/18) = (50/9) m/sec
∴ Time taken by the train to pass the man = 75 x (9/50) = 13.5 sec