RRB NTPC - Problems on Trains

81.

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: 

   A.) 150 km/hr
   B.) 50 km/hr
   C.) 75 km/hr
   D.) 55 km/hr

Answer: Option 'B'

Speed of the train relative to man = 125/10 m/sec
= 25/2 m/sec.
= 25/2 x 18/5 km/hr
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45
x = 50 km/hr.

82.

A train crosses a platform of 120m in 15sec, same train crosses another platform of length 180m in 18sec. then find the length of the train?

   A.) 175m
   B.) 180m
   C.) 185m
   D.) 170m

Answer: Option 'B'

Length of the train be ‘X’ 
X + 120/15 = X + 180/18 
6X + 720 = 5X + 900 
X = 180m

83.

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: 

   A.) 45 km/hr
   B.) 50 km/hr
   C.) 54 km/hr
   D.) 55 km/hr

Answer: Option 'B'

Given, Length of the train = 125 meter
Time taken by the train to pass the man = 10 sec
Speed of man =5 km/hr
Speed of the train relative to man = (125/10) m/sec
= (25/2)m/sec
=(25/2) x (18/5) km/hr
= 45 km/hr
Let the speed of the train be x km/hr.
Since Man and Train are moving in same direction, speeds must be subtracted
Then, relative speed = Speed of train -Speed of man
=> x - 5 = 45
=> x = 50 km/hr

84.

A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel is:

   A.) 540 m
   B.) 130 m
   C.) 500 m
   D.) 260 m

Answer: Option 'C'

Given, Length of the train = 800 m
Speed of the train = 78 km/hr (convert km/hr to m/sec)
= 78 × (5/18) m /sec
= 21.667 m /sec
=> Speed of the train = 21.667 m /sec
Time taken by the train to cross the tunnel = 1 min = 60 sec
To find the length of the tunnel:
Time taken by train to cross tunnel = (Length of tunnel + Length of train) / speed of the train
=> 60 = (Length of tunnel + 800) / 21.667
=> 60 × 21.667 = Length of tunnel + 800
=> 1300 = Length of tunnel + 800
=> 1300 – 800 = Length of tunnel
=> 500 = Length of tunnel
Thus, the Length of tunnel = 500 m

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