RRB NTPC - Problems on Trains

1.

Two trains 100 metres and 120 metres long are running in the same direction with the speeds of 72 km/hr and 54 km/hr .In how much time will the first train cross the second?

   A.) 45 second
   B.) 44.5 second
   C.) 44 second
   D.) 41.2 second

Answer: Option 'C'

44 second

2.

A train 130 m long passes a bridge in 21 sec moving with a speed of the 90 km/hr. Find the length of the bridge.

   A.) 415
   B.) 395
   C.) 405
   D.) 385

Answer: Option 'B'

Speed of the train = (Train length + Bridge Length ) / time taken to cross the bridge
=> 90 * (5/18)= (130 + Bridge Length) / 21
=> 25 =(130 + Bridge Length) / 21
=> 130 +Bridge Length = 21 x 25
=>130 +Bridge Length =525
=> Bridge Length = 525 - 130
=>Bridge Length = 395 m

3.

A train travels from City X to City Y at a speed of 44 kmph, while on its return journey the train was travelling at speed of 77 kmph. Find the average speed of the train. 

   A.) 56
   B.) 58.5
   C.) 60
   D.) 60.5

Answer: Option 'A'

Let x be the speed of the train while going from City X to Y.
Let y be the speed of the train while going from City Y to X.
Average speed of the train is given by = 2xy / (x+y) 
Average speed = (2 x 44 x 77) / (44 + 77 )
Average speed = 56

4.

A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? 

   A.) 230 m
   B.) 240 m
   C.) 260 m
   D.) 320 m

Answer: Option 'A'

Given the length of the first train = 270 metres.
Let the length of the second train be x metres
Relative speed = Speed of first train + Speed of Second Train
= (120 + 80) kmph
= ( 200 x 5/18 ) m/sec
= 1000/ 18 m/sec.
Therefore,Time taken by the first train to cross the another train = Length of two trains / Relative speed
=> 9 = [ 270 + x ] / (1000/ 18)
=> 9 = ([ 270 + x ] * 18) / 1000
=> 9 * 1000 / 18 =270 + x
=> 500 = 270 + x
=> 500 - 270 = x
=> 230 = x
Thus thelength of the second train = 230 metres

5.

A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

   A.) 5 sec
   B.) 6 sec
   C.) 7 sec
   D.) 10 sec

Answer: Option 'B'

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr. = ( 66 x 5 /18 m/sec = (55 / 3 ) m/sec
Therefore, Time taken to pass the man = ( 110 x 3/55 ) sec = 6 sec.

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