If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
Answer: B
\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]
\[ 90 \text{ kmph} = 25 \text{ m/s} \]
A pole has no length, so the train covers only itself:
\[ L = 25 \times 5 = 125 \text{ m} \]
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Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
Answer: C
Trains in the same direction close at the difference of their speeds; in opposite directions, at the sum.
\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]
\[ \text{relative speed} = 40 - 22 = 18 \text{ kmph} = 5 \text{ m/s} \]
\[ \text{combined length} = 5 \times 60 = 300 \text{ m} \]
\[ L_{2} = 300 - 125 = 175 \text{ m} \]
Passing completely means covering both lengths, which is why the first train's 125 m is subtracted at the end.
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How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Answer: C
\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]
\[ 36 \text{ kmph} = 10 \text{ m/s} \]
\[ t = \frac{100 + 150}{10} = 25 \text{ seconds} \]
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A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Answer: A
Crossing the bridge covers the train plus the bridge.
\[ v = \frac{100 + 300}{45} = \frac{400}{45} = 8.89 \text{ m/s} \]
\[ 8.89 \times \frac{18}{5} = 32 \text{ kmph} \]
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A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Answer: B
A man standing is a point, so the train covers only its own length.
\[ v = \frac{180}{6} = 30 \text{ m/s} \]
\[ 30 \times \frac{18}{5} = 108 \text{ kmph} \]
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Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Answer: C
In one hour of clock time the train covers 36 km instead of 45, losing 9 km of travel.
\[ t = \frac{9}{45} \text{ h} = \frac{1}{5} \text{ h} = 12 \text{ minutes} \]
The lost distance is timed at the running speed of 45 kmph, since that is the speed it would have been covered at.
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One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
Answer: A
\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]
Put both speeds in the same units.
\[ 45 \text{ kmph} = 45 \times \frac{5}{18} = 12.5 \text{ m/s} \]
\[ 12.5 : 10 = 5 : 4 \]
Comparing 45 with 10 directly would give the meaningless 9 : 2 - the third option.
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A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
Answer: C
The first train leaves five hours earlier, so it is
\[ 30 \times 5 = 150 \text{ km} \]
ahead at 2 p.m. The gap closes at \( 40 - 30 = 10 \) kmph:
\[ t = \frac{150}{10} = 15 \text{ hours} \]
\[ \text{distance from Delhi} = 40 \times 15 = 600 \text{ km} \]
Checking with the first train: \( 30 \times 20 = 600 \) km in the twenty hours since 9 a.m.
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How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
Answer: C
\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]
\[ 54 \text{ kmph} = 15 \text{ m/s} \]
\[ t = \frac{165 + 660}{15} = \frac{825}{15} = 55 \text{ sec} \]
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Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Answer: D
Trains in the same direction close at the difference of their speeds; in opposite directions, at the sum.
\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]
\[ \text{relative speed} = 80 + 65 = 145 \text{ kmph} = \frac{725}{18} = 40.28 \text{ m/s} \]
\[ t = \frac{121 + 165}{40.28} = \frac{286}{40.28} \approx 7.1 \text{ sec} \]
"Clear of each other" means both lengths must pass, which is why 286 m and not 165 m is the distance.
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