Problems on Trains Questions and Answers

Q: A train 150 m long is running at 72 km/hr. How long will it take to cross a pole ?

Correct answer: 7.5 secondsConvert the speed to metres per second by multiplying by \(\tfrac{5}{18}\).\[72 \times \frac{5}{18} = 20 \text{ m/s}\]Crossing a pole means covering just the train’s own length, since a pole has no length of its own.\[t = \frac{150}{20} = 7.5 \text{ seconds}\]

Q: A train 240 m long crosses a bridge in 30 seconds while running at 72 km/hr. What is the length of the bridge ?

Correct answer: 360 m\[\text{Speed} = 72 \times \frac{5}{18} = 20 \text{ m/s}\]\[\text{Total distance covered} = 20 \times 30 = 600 \text{ m}\]That total is the train plus the bridge, so the bridge is \(600 - 240 = 360\) m.

Q: A train 200 m long crosses a platform 300 m long in 25 seconds. What is its speed ?

Correct answer: 72 km/hrTo clear a platform the train must cover its own length plus the platform’s.\[\text{Distance} = 200 + 300 = 500 \text{ m}, \qquad \text{Speed} = \frac{500}{25} = 20 \text{ m/s}\]\[20 \times \frac{18}{5} = 72 \text{ km/hr}\]

Q: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 45 \text{ km/hr} = 12.5 \text{ m/s} \]\[ \text{total distance} = 12.5 \times 30 = 375 \text{ m} \]\[ \text{bridge} = 375 - 130 = 245 \text{ m} \]That total covers the train plus the bridge, so the train's own length is subtracted at the end.

Q: A train crosses a platform 250 m long in 30 seconds and a signal pole in 15 seconds. What is the length of the train ?

Correct answer: 250 mLet the length be \(L\) and the speed \(v\). Passing the pole covers \(L\), and passing the platform covers \(L + 250\).\[\frac{L}{v} = 15, \qquad \frac{L + 250}{v} = 30\]Subtracting, \(\tfrac{250}{v} = 15\), so \(v = \tfrac{50}{3}\) m/s and \(L = 15 \times \tfrac{50}{3} = 250\) m.The extra 15 seconds is exactly the time to cover the platform alone.

Q: A train running at 60 km/hr overtakes a man walking at 6 km/hr in the same direction and passes him in 12 seconds. What is the length of the train ?

Correct answer: 180 mSince both move the same way, the speeds subtract.\[60 - 6 = 54 \text{ km/hr} = 54 \times \frac{5}{18} = 15 \text{ m/s}\]Passing a man means covering only the train’s length.\[L = 15 \times 12 = 180 \text{ m}\]

Q: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

A signal pole is a point, so that crossing gives the speed.\[ v = \frac{300}{18} = \frac{50}{3} \text{ m/s} \]\[ \text{total distance over the platform} = \frac{50}{3} \times 39 = 650 \text{ m} \]\[ \text{platform} = 650 - 300 = 350 \text{ m} \]The data are complete, so "data inadequate" is a trap; 650 m is the combined distance, not the platform.

Q: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 90 \text{ km/hr} = 25 \text{ m/s} \]In one minute the train covers\[ 25 \times 60 = 1500 \text{ m} \]That is the train plus the platform, and the two are equal:\[ 2L = 1500 \quad\Longrightarrow\quad L = 750 \text{ metres} \]

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81.

Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

A.2 : 3
B.4 : 3
C.6 : 7
D.9 : 16

Answer: B

Two trains that meet and then take \( t_{1} \) and \( t_{2} \) to finish have speeds in the ratio

\[ \frac{v_{1}}{v_{2}} = \sqrt{\frac{t_{2}}{t_{1}}} \]

\[ = \sqrt{\frac{16}{9}} = \frac{4}{3} \quad\Longrightarrow\quad 4 : 3 \]

The square root is essential; taking the times directly would give 9 : 16, which is offered as the last option and is also the wrong way round.

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82.

A train 150 m long is running at 72 km/hr. How long will it take to cross a pole ?

A.6 seconds
B.7.5 seconds
C.9 seconds
D.10 seconds

Answer: C

Correct answer: 7.5 seconds

Convert the speed to metres per second by multiplying by \(\tfrac{5}{18}\).

\[72 \times \frac{5}{18} = 20 \text{ m/s}\]

Crossing a pole means covering just the train’s own length, since a pole has no length of its own.

\[t = \frac{150}{20} = 7.5 \text{ seconds}\]

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83.

A train 240 m long crosses a bridge in 30 seconds while running at 72 km/hr. What is the length of the bridge ?

A.300 m
B.340 m
C.360 m
D.400 m

Answer: D

Correct answer: 360 m

\[\text{Speed} = 72 \times \frac{5}{18} = 20 \text{ m/s}\]

\[\text{Total distance covered} = 20 \times 30 = 600 \text{ m}\]

That total is the train plus the bridge, so the bridge is \(600 - 240 = 360\) m.

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84.

A train 200 m long crosses a platform 300 m long in 25 seconds. What is its speed ?

A.60 km/hr
B.66 km/hr
C.72 km/hr
D.80 km/hr

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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85.

The length of the bridge, which a train 130 meters 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: C

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]

\[ 45 \text{ km/hr} = 12.5 \text{ m/s} \]

\[ \text{total distance} = 12.5 \times 30 = 375 \text{ m} \]

\[ \text{bridge} = 375 - 130 = 245 \text{ m} \]

That total covers the train plus the bridge, so the train's own length is subtracted at the end.

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86.

A train crosses a platform 250 m long in 30 seconds and a signal pole in 15 seconds. What is the length of the train ?

A.200 m
B.225 m
C.250 m
D.300 m

Answer: B

Correct answer: 250 m

Let the length be \(L\) and the speed \(v\). Passing the pole covers \(L\), and passing the platform covers \(L + 250\).

\[\frac{L}{v} = 15, \qquad \frac{L + 250}{v} = 30\]

Subtracting, \(\tfrac{250}{v} = 15\), so \(v = \tfrac{50}{3}\) m/s and \(L = 15 \times \tfrac{50}{3} = 250\) m.

The extra 15 seconds is exactly the time to cover the platform alone.

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87.

A train running at 60 km/hr overtakes a man walking at 6 km/hr in the same direction and passes him in 12 seconds. What is the length of the train ?

A.150 m
B.165 m
C.180 m
D.200 m

Answer: B

Correct answer: 180 m

Since both move the same way, the speeds subtract.

\[60 - 6 = 54 \text{ km/hr} = 54 \times \frac{5}{18} = 15 \text{ m/s}\]

Passing a man means covering only the train’s length.

\[L = 15 \times 12 = 180 \text{ m}\]

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88.

A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

A.150 m
B.200 m
C.350 m
D.400 m

Answer: C

A signal pole is a point, so that crossing gives the speed.

\[ v = \frac{300}{18} = \frac{50}{3} \text{ m/s} \]

\[ \text{total distance over the platform} = \frac{50}{3} \times 39 = 650 \text{ m} \]

\[ \text{platform} = 650 - 300 = 350 \text{ m} \]

The data are complete, so "data inadequate" is a trap; 650 m is the combined distance, not the platform.

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89.

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.180 m
B.200 m
C.240 m
D.320 m

Answer: C

Speed = [54 * 5/18] m/sec = 15 m/sec.

Length of the train = (15 * 20) m = 300 m.

Let the length of the platform be x meters.

Then, x + 300 / 36 = 15

x + 300 = 540

x = 240 m.

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90.

The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:

A.850
B.525
C.550
D.750

Answer: D

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]

\[ 90 \text{ km/hr} = 25 \text{ m/s} \]

In one minute the train covers

\[ 25 \times 60 = 1500 \text{ m} \]

That is the train plus the platform, and the two are equal:

\[ 2L = 1500 \quad\Longrightarrow\quad L = 750 \text{ metres} \]

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