Problems on Trains Questions and Answers

Q: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. 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: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 60 \text{ km/hr} = 60 \times \frac{5}{18} = \frac{50}{3} \text{ m/s} \]A pole has no length, so the train covers only itself:\[ L = \frac{50}{3} \times 9 = 150 \text{ metres} \]

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: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 72 \text{ km/hr} = 20 \text{ m/s} \]\[ t = \frac{110 + 132}{20} = \frac{242}{20} = 12.1 \text{ seconds} \]Both the train and the bridge must be cleared, so their lengths add.

Q: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 60 \text{ km/hr} = \frac{50}{3} \text{ m/s} \]\[ L = \frac{50}{3} \times 9 = 150 \text{ m} \]150 m is not among the listed values, so the answer is none of these. The data are complete, which rules out "cannot be determined".

Q: How long does a train 90 metres long running at the speed of 71 km/hr take to cross a bridge 132 metres in length?

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 71 \text{ km/hr} = 71 \times \frac{5}{18} = 19.72 \text{ m/s} \]\[ t = \frac{90 + 132}{19.72} = \frac{222}{19.72} = 11.26 \text{ seconds} \]Crossing a bridge covers the train plus the bridge; the train's own 90 m must not be dropped.

Q: A train takes 20 seconds to pass completely through a station 160 m long and 15 seconds through another station 110 m long. Find the length of the train.

Each crossing covers the train's length plus the station's.\[ L + 160 = 20v, \qquad L + 110 = 15v \]Subtracting:\[ 50 = 5v \quad\Longrightarrow\quad v = 10 \text{ m/s} \]\[ L = 20 \times 10 - 160 = 40 \text{ m} \]Subtracting the two equations eliminates the unknown length in one step.

Q: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

The man walks the same way, so the speeds subtract.\[ \text{relative speed} = 63 - 3 = 60 \text{ km/hr} = 60 \times \frac{5}{18} = \frac{50}{3} \text{ m/s} \]\[ t = \frac{500 \times 3}{50} = 30 \text{ seconds} \]Only the train's own length counts, since the man occupies a single point.

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21.

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

A.320 m
B.350 m
C.650 m
D.None of these

Answer: B

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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22.

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.

A.150 m
B.145 m
C.140 m
D.135 m

Answer: A

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

\[ 60 \text{ km/hr} = 60 \times \frac{5}{18} = \frac{50}{3} \text{ m/s} \]

A pole has no length, so the train covers only itself:

\[ L = \frac{50}{3} \times 9 = 150 \text{ metres} \]

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23.

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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24.

How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?

A.9.8 sec
B.12.1 sec
C.12.42 sec
D.14.3 sec

Answer: B

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

\[ 72 \text{ km/hr} = 20 \text{ m/s} \]

\[ t = \frac{110 + 132}{20} = \frac{242}{20} = 12.1 \text{ seconds} \]

Both the train and the bridge must be cleared, so their lengths add.

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25.

A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?

A.120 m
B.None of these
C.Cannot be determined
D.324 m

Answer: B

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

\[ 60 \text{ km/hr} = \frac{50}{3} \text{ m/s} \]

\[ L = \frac{50}{3} \times 9 = 150 \text{ m} \]

150 m is not among the listed values, so the answer is none of these. The data are complete, which rules out "cannot be determined".

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26.

How long does a train 90 metres long running at the speed of 71 km/hr take to cross a bridge 132 metres in length?

A.9.8 sec
B.11.26 sec
C.12.42 sec
D.14.3 sec

Answer: B

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

\[ 71 \text{ km/hr} = 71 \times \frac{5}{18} = 19.72 \text{ m/s} \]

\[ t = \frac{90 + 132}{19.72} = \frac{222}{19.72} = 11.26 \text{ seconds} \]

Crossing a bridge covers the train plus the bridge; the train's own 90 m must not be dropped.

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27.

Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

A.9 a.m.
B.10 a.m.
C.10.30 a.m.
D.11 a.m.

Answer: B

Suppose they meet x hours after 7 a.m.

Distance covered by A in x hours = 20x km.

Distance covered by B in (x - 1) hours = 25(x - 1) km.

20x + 25(x - 1) = 110

" src="https://www.indiabix.com/_files/images/aptitude/1-sym-imp.gif" /> 45x = 135

" src="https://www.indiabix.com/_files/images/aptitude/1-sym-imp.gif" /> x = 3.

So, they meet at 10 a.m.

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28.

A train takes 20 seconds to pass completely through a station 160 m long and 15 seconds through another station 110 m long. Find the length of the train.

A.100 m
B.70 m
C.60 m
D.40 m

Answer: D

Each crossing covers the train's length plus the station's.

\[ L + 160 = 20v, \qquad L + 110 = 15v \]

Subtracting:

\[ 50 = 5v \quad\Longrightarrow\quad v = 10 \text{ m/s} \]

\[ L = 20 \times 10 - 160 = 40 \text{ m} \]

Subtracting the two equations eliminates the unknown length in one step.

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29.

How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

A.25 sec
B.28 sec
C.30 sec
D.35 sec

Answer: C

Let length of tunnel is x meter

Distance = 800+x meter

Time = 1 minute = 60 seconds

Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s

Distance = Speed*Time

800+x = (65/3) * 60

800+x = 20 * 65 = 1300

x = 1300 - 800 = 500 meters

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30.

How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

A.25
B.30
C.40
D.45

Answer: B

The man walks the same way, so the speeds subtract.

\[ \text{relative speed} = 63 - 3 = 60 \text{ km/hr} = 60 \times \frac{5}{18} = \frac{50}{3} \text{ m/s} \]

\[ t = \frac{500 \times 3}{50} = 30 \text{ seconds} \]

Only the train's own length counts, since the man occupies a single point.

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