Problems on Trains

km/hr to m/s conversion: a km/hr = a x 5 m/s. 18 m/s to km/hr conversion: a m/s = a x 18 km/hr. 5 Formulas for finding Speed, Time and Distance Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres. Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres. Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s. Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s. If two trains of length a metres and b metres are moving in opposite directions at um/s and v m/s, then: The time taken by the trains to cross each other = (a + b) sec. (u + v) If two trains of length a metres and b metres are moving in the same direction at um/s and v m/s, then: The time taken by the faster train to cross the slower train = (a + b) sec. (u - v) If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed)

1.	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 metres B. 180 metres C. 324 metres D. 150 metres Answer & Explanation Answer: Option D Explanation: Speed= 60 x 5 m/sec = 50 m/sec. 18 3 Length of the train = (Speed x Time) = 50 x 9 m = 150 m.

2.	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 & Explanation Answer: Option B Explanation: Speed of the train relative to man = 125 m/sec 10    = 25 m/sec. 2    = 25 x 18 km/hr 2 5    = 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.

3.	The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
	A. 200 m B. 225 m C. 245 m D. 250 m Answer & Explanation Answer: Option C Explanation: Speed = 45 x 5 m/sec = 25 m/sec. 18 2 Time = 30 sec. Let the length of bridge be x metres. Then, 130 + x = 25 30 2  2(130 + x) = 750  x = 245 m.

4.	Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
	A. 1 : 3 B. 3 : 2 C. 3 : 4 D. None of these Answer & Explanation Answer: Option B Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27x metres, and length of the second train = 17y metres. 27x + 17y = 23 x+ y  27x + 17y = 23x + 23y  4x = 6y x = 3 . y 2

5.	A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
	A. 120 m B. 240 m C. 300 m D. None of these Answer & Explanation Answer: Option B Explanation: Speed = 54 x 5 m/sec = 15 m/sec. 18 Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, x + 300 = 15 36  x + 300 = 540  x = 240 m.