Train Problems Set 1
Formulas
 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  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 u m/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 u m/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) = (b : a)
1. 
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
 
Answer: Option D
Explanation:
Length of the train = (Speed x Time).

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:
 
Answer: Option B
Explanation:
= 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:
 
Answer: Option C
Explanation:
Time = 30 sec.
Let the length of bridge be x metres.
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:
 
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 = 23x + 23y
4x = 6y

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?
 
Answer: Option B
Explanation:
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
x + 300 = 540
x = 240 m.

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