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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