PROBLEMS ON TRAINS PRACTICE QUESTIONS

Question 1 :

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long ?

(A)  40 sec  (B)  42 sec  (C)  45 sec  (D)  48 sec

Solution :

First let us convert the speed from km/hr to m/sec.

45 km/hr  =  45⋅(5/18) m/sec

  =  5⋅(5/2) m/sec

  =  (25/2) m/sec

Time taken by the train of length b meters to cross a bridge of length l meters is equal to the time taken the by train to cross the distance (l + b) meters.

Total distance to be covered  = 360 + 140

  =  500 m

Time  =   Distance / Speed

=  500/(25/2)

Time  =  40 seconds

Question 2 :

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train ?

(A)  120 m  (B)  180 m   (C)  150 m  (D)  None of these

Solution :

Time taken by the train of length l meters to cross of a pole is equal to the time taken by the train to cover the distance l meter.

Let x be the length of the train.

Converting the speed from km/hr to m/sec, we get

  =  60⋅(5/18) m/sec

  =  (50/3) m/sec

Time  =  Distance / Speed

9  =  x / (50/3)

x  =  9⋅(50/3)

x  =  150 m

So, the length of the train is 150 m.

Question 3 :

A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is .

Solution :

Let x be the length of the train.

Time taken to cross a telegraph post  =  6 seconds

1000 m  =  1 km

12 km  =  12000 m

Distance covered  =  x + 12000

Time taken  =  10 minutes  =  600 seconds

(x + 12000) / Speed  =  600  

Speed  =  (x + 12000)/600  ------(1)

x / Speed  =  6  

Speed  =  x/6  ------(2)

(1)  =  (2)

(x + 12000) / 600  =  x / 6

6(x + 12000)  =  600x 

600x - 6x  =  72000

594x  =  72000

x  =  121 m

So, the length of the train is 121 m.

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