Two trains 120 m and 180 m long are running in opposite directions at 54 km/hr and 36 km/hr. How long will they take to cross each other ?
Answer: A
Correct answer: 12 seconds
Moving in opposite directions, the speeds add.
\[54 + 36 = 90 \text{ km/hr} = 90 \times \frac{5}{18} = 25 \text{ m/s}\]
They must together cover the sum of their lengths, 300 m.
\[t = \frac{300}{25} = 12 \text{ seconds}\]
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A train 200 m long crosses a platform 300 m long in 25 seconds. What is its speed ?
Answer: B
Correct answer: 72 km/hr
To clear a platform the train must cover its own length plus the platform’s.
\[\text{Distance} = 200 + 300 = 500 \text{ m}, \qquad \text{Speed} = \frac{500}{25} = 20 \text{ m/s}\]
\[20 \times \frac{18}{5} = 72 \text{ km/hr}\]
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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: B
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
\[ 54 \text{ km/hr} = 15 \text{ m/s} \]
The man is a point, so that crossing gives the train's length:
\[ L = 15 \times 20 = 300 \text{ m} \]
The platform crossing covers train plus platform:
\[ 15 \times 36 = 540 \quad\Longrightarrow\quad P = 540 - 300 = 240 \text{ m} \]
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A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Answer: C
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
\[ 45 \text{ km/hr} = 12.5 \text{ m/s} \]
\[ t = \frac{360 + 140}{12.5} = \frac{500}{12.5} = 40 \text{ seconds} \]
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A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Answer: B
The man walks toward the train, so the speeds add.
\[ \text{relative speed} = 60 + 6 = 66 \text{ kmph} = 66 \times \frac{5}{18} = \frac{55}{3} \text{ m/s} \]
A man is a point, so only the train's own length is covered:
\[ t = \frac{110 \times 3}{55} = 6 \text{ seconds} \]
Had he walked the same way as the train, the relative speed would be 54 kmph and the answer about 7.3 seconds.
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A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Answer: C
An electric pole has no length, so the train covers only its own 400 m.
\[ v = \frac{400}{20} = 20 \text{ m/s} \]
\[ 20 \times \frac{18}{5} = 72 \text{ Kmph} \]
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A man walks with 3kmph speed in the direction of a train. How much time will a 500m long train take to overtake him at a speed of 63kmph?
Answer: B
Distance to be covered = 500 metres
Effective speed will be equal to difference in the speed of ma and train as they move in opposite directions.
Thus, effective speed = 63kmph-3kmph= 60kmph.
60kmph is equal to 50/3 m/s.
Time = Distance/ Speed
Thus, time taken will be equal to 500/(50/3).
On solving, time = 30 seconds.
Therefore, the train will take 30 seconds to overtake the man.
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A train passes a telegraph post in 8 seconds and a 264 m long bridge in 20 seconds. What is the length of the train
Answer: B
A telegraph post has no length, so the first crossing covers only the train.
\[ L = 8v \]
The bridge crossing covers the train plus 264 m:
\[ L + 264 = 20v \]
Substituting the first into the second:
\[ 8v + 264 = 20v \quad\Longrightarrow\quad 12v = 264 \quad\Longrightarrow\quad v = 22 \text{ m/s} \]
\[ L = 8 \times 22 = 176 \text{ m} \]
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