# Problems on Trains

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Problems on Trains:

• a km/hr = a*(5/18) m/s
• a m/s = a*(18/5) km/hr
• Time taken by a train of length l metres to pass a pole or a 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 stationary object of length b metres is the time taken by the train to cover (l + b) metres.
• Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed = (u – v) m/s.
• Suppose two trains or two bodies are moving in the opposite direction 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 time taken by the trains to cross each other = (a+b)/(u+v) sec.
• If two trains of length a metres and b metres are moving in same directions at u m/s and v m/s, then time taken by the f*er train to cross the slower train = (a+b)/(u-v) sec.
• If two trains 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 )

# Aptitude Questions (Problems on Trains):

1. A train moves with a speed of 108 kmph. Its speed in metres per second is:

A)    10.8

B)    18

C)    30

D)    38.8

E)    None of these

Explanation:

108 kmph = (108*5/18) m/s = 30 m/sec

2. A train 280 m long, running with a speed of 63 km/hr will pass a tree in:

A)    15 sec

B)    16 sec

C)    18 sec

D)    20 sec

E)    None of these

Explanation:

Speed = (63*5/18) m/sec = 35/2 m/sec

Time taken = (280*2/35) sec = 16 sec

3. 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

E)    None of these

Explanation:

Speed = (60*5/18) m/sec = 50/3 m/sec

Length of the train = (speed * time) = (50/3*9) m = 150 m

4. A train covers a distance of 12 km in 10 minutes and if it takes 7 seconds to pass a pole, then the length of the train is:

A)    90 m

B)    100 m

C)    120 m

D)    140 m

E)    None of these

Explanation:

Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec

Length of the train = (speed * time) = (20 * 7) m = 140 m

5. The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

A)    200 m

B)    225 m

C)    235 m

D)    250 m

E)    None of these

Explanation:

Speed = (45 * 5/18) m/sec = 25/2 m/sec; Time = 30 sec

Let the length of bridge be x metres.

Then, (140+x) / 30 = 25/2 <=> 2(140 + x) = 750 <=> x = 235 m