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: 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?

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

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: Two trains with lengths 126 m and 119 m respectively are moving towards each other. Their speeds are 12 m/s and 23 m/s, respectively. What will be the time needed by the trains to cross each other?

Trains moving in the same direction close at the difference of their speeds; in opposite directions, at the sum.\[ \text{relative speed} = 12 + 23 = 35 \text{ m/s} \]\[ t = \frac{126 + 119}{35} = \frac{245}{35} = 7 \text{ seconds} \]The speeds are already in m/s, so no conversion is needed.

Q: Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

Trains moving in the same direction close at the difference of their speeds; in opposite directions, at the sum.\[ \text{relative speed} = \frac{120 + 120}{12} = 20 \text{ m/s} \]Both trains have the same speed \( v \), so\[ 2v = 20 \quad\Longrightarrow\quad v = 10 \text{ m/s} = 10 \times \frac{18}{5} = 36 \text{ km/hr} \]Forgetting to halve the relative speed gives 72 km/hr - the last option.

Q: Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 60 km more than the other. What is the distance between the two stations?

The extra 60 km comes from the difference in speeds.\[ 25t - 20t = 60 \quad\Longrightarrow\quad 5t = 60 \quad\Longrightarrow\quad t = 12 \text{ h} \]They approach at \( 20 + 25 = 45 \) km/hr:\[ D = 45 \times 12 = 540 \text{ km} \]Checking: 240 km and 300 km, differing by exactly 60.

Q: Two trains A and B leave Kolkata for Sikkim at 8:00 pm and 8:30 pm respectively and run at 90 km/hr and 120 km/hr, respectively. At what distance from Kolkata, will the two trains meet?

The first train has a half-hour head start.\[ \text{lead at 8:30} = 90 \times 0.5 = 45 \text{ km} \]The second closes at \( 120 - 90 = 30 \) km/hr:\[ t = \frac{45}{30} = 1.5 \text{ h} \]\[ \text{distance from Kolkata} = 120 \times 1.5 = 180 \text{ km} \]Checking with the first train: \( 90 \times 2 = 180 \) km in the two hours since 8 pm.

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61.

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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62.

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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63.

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

A.66 km/hr
B.72 km/hr
C.78 km/hr
D.81 km/hr

Answer: D

Both walkers move the same way as the train, so the relative speeds are differences.

\[ L = (v - 4.5) \times \frac{5}{18} \times 8.4 = (v - 5.4) \times \frac{5}{18} \times 8.5 \]

\[ 8.4(v - 4.5) = 8.5(v - 5.4) \]

\[ 8.4v - 37.8 = 8.5v - 45.9 \quad\Longrightarrow\quad 0.1v = 8.1 \]

\[ v = 81 \text{ km/hr} \]

The train's length works out at 75.6 m, though the question asks only for the speed.

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64.

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

A.50 m
B.150 m
C.200 m
D.Data inadequate

Answer: B

The pole crossing covers the train alone, the platform crossing the train plus 100 m.

\[ L = 15v, \qquad L + 100 = 25v \]

Subtracting:

\[ 100 = 10v \quad\Longrightarrow\quad v = 10 \text{ m/s} \]

\[ L = 15 \times 10 = 150 \text{ m} \]

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65.

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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66.

Two trains with lengths 126 m and 119 m respectively are moving towards each other. Their speeds are 12 m/s and 23 m/s, respectively. What will be the time needed by the trains to cross each other?

A.35 seconds
B.11 seconds
C.210 seconds
D.7 seconds

Answer: D

Trains moving in the same direction close at the difference of their speeds; in opposite directions, at the sum.

\[ \text{relative speed} = 12 + 23 = 35 \text{ m/s} \]

\[ t = \frac{126 + 119}{35} = \frac{245}{35} = 7 \text{ seconds} \]

The speeds are already in m/s, so no conversion is needed.

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67.

Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

A.10
B.18
C.36
D.72

Answer: C

Trains moving in the same direction close at the difference of their speeds; in opposite directions, at the sum.

\[ \text{relative speed} = \frac{120 + 120}{12} = 20 \text{ m/s} \]

Both trains have the same speed \( v \), so

\[ 2v = 20 \quad\Longrightarrow\quad v = 10 \text{ m/s} = 10 \times \frac{18}{5} = 36 \text{ km/hr} \]

Forgetting to halve the relative speed gives 72 km/hr - the last option.

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68.

Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 60 km more than the other. What is the distance between the two stations?

A.620 km
B.540 km
C.460 km
D.720 km

Answer: B

The extra 60 km comes from the difference in speeds.

\[ 25t - 20t = 60 \quad\Longrightarrow\quad 5t = 60 \quad\Longrightarrow\quad t = 12 \text{ h} \]

They approach at \( 20 + 25 = 45 \) km/hr:

\[ D = 45 \times 12 = 540 \text{ km} \]

Checking: 240 km and 300 km, differing by exactly 60.

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69.

Two trains A and B leave Kolkata for Sikkim at 8:00 pm and 8:30 pm respectively and run at 90 km/hr and 120 km/hr, respectively. At what distance from Kolkata, will the two trains meet?

A.450 kms
B.180 kms
C.150 kms
D.360 kms

Answer: B

The first train has a half-hour head start.

\[ \text{lead at 8:30} = 90 \times 0.5 = 45 \text{ km} \]

The second closes at \( 120 - 90 = 30 \) km/hr:

\[ t = \frac{45}{30} = 1.5 \text{ h} \]

\[ \text{distance from Kolkata} = 120 \times 1.5 = 180 \text{ km} \]

Checking with the first train: \( 90 \times 2 = 180 \) km in the two hours since 8 pm.

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70.

The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?

A.58 Kmph
B.68 Kmph
C.78 Kmph
D.55 Kmph

Answer: B

Length of the two trains = 600m + 400m

Speed of the first train = X

Speed of the second train= 48 Kmph

1000/X - 48 = 180

1000/x - 48 * 5/18 = 180

50 = 9X - 120

X = 68 Kmph

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