Problems on Trains Questions and Answers

Q: Two trains of equal length run on parallel tracks in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower one in 36 seconds. What is the length of each train ?

Correct answer: 50 mThe relative speed is the difference, since they travel the same way.\[46 - 36 = 10 \text{ km/hr} = 10 \times \frac{5}{18} = \frac{25}{9} \text{ m/s}\]\[\text{Distance covered} = \frac{25}{9} \times 36 = 100 \text{ m}\]That 100 m is the combined length of both trains, so each is 50 m long.

Q: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 144 \text{ km/hr} = 144 \times \frac{5}{18} = 40 \text{ m/s} \]An electric pole has no length, so only the train's own 100 m is covered:\[ t = \frac{100}{40} = 2.5 \text{ seconds} \]

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

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 63 \text{ km/hr} = 63 \times \frac{5}{18} = 17.5 \text{ m/s} \]A tree is a point, so the train covers only its own length:\[ t = \frac{280}{17.5} = 16 \text{ seconds} \]The conversion is where the answer is decided: at 17.5 m/s the 280 m takes exactly 16 seconds, not 15.

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: 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 ?

Correct answer: 12 secondsMoving 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.\[t = \frac{300}{25} = 12 \text{ seconds}\]

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: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?

Find the speed from the long run, then use it on the post.\[ v = \frac{12 \text{ km}}{10 \text{ min}} = \frac{12000}{600} = 20 \text{ m/s} \]A telegraph post is a point, so the 6 seconds covers only the train:\[ L = 20 \times 6 = 120 \text{ m} \]Converting 12 km in 10 minutes to 72 km/hr and then to m/s gives the same 20.

Q: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec 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 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 78 \text{ km/hr} = 78 \times \frac{5}{18} = \frac{65}{3} \text{ m/s} \]\[ \text{total distance in 60 s} = \frac{65}{3} \times 60 = 1300 \text{ m} \]\[ \text{tunnel} = 1300 - 800 = 500 \text{ metres} \]

Important Instructions

101.

Two trains of equal length run on parallel tracks in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower one in 36 seconds. What is the length of each train ?

A.50 m
B.72 m
C.80 m
D.82 m

Answer: B

Correct answer: 50 m

The relative speed is the difference, since they travel the same way.

\[46 - 36 = 10 \text{ km/hr} = 10 \times \frac{5}{18} = \frac{25}{9} \text{ m/s}\]

\[\text{Distance covered} = \frac{25}{9} \times 36 = 100 \text{ m}\]

That 100 m is the combined length of both trains, so each is 50 m long.

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102.

In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?

A.2.5 sec
B.4.25 sec
C.5 sec
D.12.5 sec

Answer: A

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

\[ 144 \text{ km/hr} = 144 \times \frac{5}{18} = 40 \text{ m/s} \]

An electric pole has no length, so only the train's own 100 m is covered:

\[ t = \frac{100}{40} = 2.5 \text{ seconds} \]

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103.

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

Answer: B

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

\[ 63 \text{ km/hr} = 63 \times \frac{5}{18} = 17.5 \text{ m/s} \]

A tree is a point, so the train covers only its own length:

\[ t = \frac{280}{17.5} = 16 \text{ seconds} \]

The conversion is where the answer is decided: at 17.5 m/s the 280 m takes exactly 16 seconds, not 15.

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104.

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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105.

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 ?

A.10 seconds
B.12 seconds
C.15 seconds
D.18 seconds

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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106.

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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107.

A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?

A.90 m
B.100 m
C.120 m
D.140 m

Answer: C

Find the speed from the long run, then use it on the post.

\[ v = \frac{12 \text{ km}}{10 \text{ min}} = \frac{12000}{600} = 20 \text{ m/s} \]

A telegraph post is a point, so the 6 seconds covers only the train:

\[ L = 20 \times 6 = 120 \text{ m} \]

Converting 12 km in 10 minutes to 72 km/hr and then to m/s gives the same 20.

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108.

A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?

A.65 sec
B.89 sec
C.100 sec
D.150 sec

Answer: B

A pole has no length, so the first crossing gives the speed.

\[ v = \frac{240}{24} = 10 \text{ m/s} \]

\[ t = \frac{240 + 650}{10} = \frac{890}{10} = 89 \text{ seconds} \]

Using only the platform's 650 m would give 65 seconds - the first distractor.

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109.

The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec 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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110.

A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?

A.130 m
B.360 m
C.500 m
D.540 m

Answer: C

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

\[ 78 \text{ km/hr} = 78 \times \frac{5}{18} = \frac{65}{3} \text{ m/s} \]

\[ \text{total distance in 60 s} = \frac{65}{3} \times 60 = 1300 \text{ m} \]

\[ \text{tunnel} = 1300 - 800 = 500 \text{ metres} \]

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