Problems on Trains Questions and Answers

Q: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is 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: The length of the bridge, which a train 130 metres 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 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?

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 54 \text{ km/hr} = 15 \text{ m/s} \]The man is a point, so that crossing gives the train's length:\[ L = 15 \times 20 = 300 \text{ m} \]The platform crossing covers train plus platform:\[ 15 \times 36 = 540 \quad\Longrightarrow\quad P = 540 - 300 = 240 \text{ m} \]

Q: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]\[ 45 \text{ km/hr} = 12.5 \text{ m/s} \]\[ t = \frac{360 + 140}{12.5} = \frac{500}{12.5} = 40 \text{ seconds} \]

Important Instructions

51.

Two trains are moving in the same direction at 50 km/hr and 30 km/hr. The faster train crosses a man in the slower train in 18 seconds. Find the length of faster train.

A.125 meter
B.100 meter
C.110 meter
D.None of these

Answer: B

Crossing a man in the other train covers only the faster train's length.

\[ \text{relative speed} = 50 - 30 = 20 \text{ km/hr} = 20 \times \frac{5}{18} = \frac{50}{9} \text{ m/s} \]

\[ L = \frac{50}{9} \times 18 = 100 \text{ m} \]

The slower train's length is irrelevant, because the reference point is a single person, not the whole train.

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52.

Find the ratio of speed of truck to train if truck covers 550m in 1 minute and train covers 33 km in 45 min.

A.4:3
B.3:4
C.2:1
D.1:2

Answer: B

Using the formula, speed=distance/time

Speed of truck = 550/60 m/s

Speed of train= 33000/(45*60) m/s

Ratio of speed of truck to train= (550/60 ) / [33000/(45*60)]

=3:4

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53.

A man walks with 3kmph speed in the direction of a train. How much time will a 500m long train take to overtake him at a speed of 63kmph?

A.42 seconds
B.30 seconds
C.50 seconds
D.36 seconds

Answer: B

Distance to be covered = 500 metres

Effective speed will be equal to difference in the speed of ma and train as they move in opposite directions.

Thus, effective speed = 63kmph-3kmph= 60kmph.

60kmph is equal to 50/3 m/s.

Time = Distance/ Speed

Thus, time taken will be equal to 500/(50/3).

On solving, time = 30 seconds.

Therefore, the train will take 30 seconds to overtake the man.

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54.

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

A.120 metres
B.180 metres
C.324 metres
D.150 metres

Answer: D

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

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

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

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

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55.

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A.45 km/hr
B.50 km/hr
C.54 km/hr
D.55 km/hr

Answer: B

The man runs the same way, so the train closes on him at the difference of the speeds and covers only its own length.

\[ \text{relative speed} = \frac{125}{10} = 12.5 \text{ m/s} = 12.5 \times \frac{18}{5} = 45 \text{ km/hr} \]

\[ v_{\text{train}} = 45 + 5 = 50 \text{ km/hr} \]

The man's speed is added back because it had been subtracted to give the relative speed.

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56.

The length of the bridge, which a train 130 metres 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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57.

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.120 m
B.240 m
C.300 m
D.None of these

Answer: B

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

\[ 54 \text{ km/hr} = 15 \text{ m/s} \]

The man is a point, so that crossing gives the train's length:

\[ L = 15 \times 20 = 300 \text{ m} \]

The platform crossing covers train plus platform:

\[ 15 \times 36 = 540 \quad\Longrightarrow\quad P = 540 - 300 = 240 \text{ m} \]

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58.

A train 240 m long passes a pole in 24 seconds. 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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59.

Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

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

Answer: A

Overtaking covers both trains' lengths at the difference of the speeds.

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

\[ 2L = \frac{25}{9} \times 36 = 100 \text{ m} \]

\[ L = 50 \text{ m} \]

The 100 m is the combined length; each train is half of it.

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60.

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

A.40 sec
B.42 sec
C.45 sec
D.48 sec

Answer: A

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

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

\[ t = \frac{360 + 140}{12.5} = \frac{500}{12.5} = 40 \text{ seconds} \]

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