Question 1

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

Accepted Answer

Step 1: Understand what's given Train A length = 140 meters Train B length = 160 meters Speed of Train A = 60 km/h Speed of Train B = 40 km/h They are moving in opposite directions on parallel tracks. Step 2: Use relative speed Since they are moving in opposite directions, we add their speeds: 
Relative speed = 60 + 40 = 100 km/h
Convert km/h to m/s: 100 × (1000 / 3600) = 100 × 5/18 = 27.78 m/s
 Step 3: Total distance to be covered They will completely cross each other when they cover the sum of their lengths: 
Total distance = 140 + 160 = 300 meters
 Step 4: Calculate time 
Time = Distance / Speed = 300 / 27.78 ≈ 10.8 seconds
 Answer: Approximately 10.8 seconds Therefore, the two trains will take about 10.8 seconds to completely cross each other. This is a typical question on trains involving relative speed. Always remember to: Convert km/h to m/s when using meters. Add speeds when objects move in opposite directions. Use total length when two objects need to fully cross each other. Such questions are important in aptitude tests and competitive exams.

Question 2

How many seconds will a 500 metre 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?

Accepted Answer

Step 1: Understand what's given Length of the train = 500 meters Speed of the train = 63 km/h Speed of the man = 3 km/h The man is walking in the same direction as the train. Step 2: Use relative speed When two objects move in the same direction, we subtract their speeds: 
Relative speed = 63 - 3 = 60 km/h
Convert to m/s: 60 × (1000 / 3600) = 60 × 5/18 = 16.67 m/s
 Step 3: Calculate time to cross Time = Distance / Speed 
Time = 500 / 16.67 ≈ 30 seconds
 Answer: The train will take approximately 30 seconds to cross the man. This problem is a classic example of relative motion, where: Same direction → subtract speeds Opposite direction → add speeds These concepts are frequently tested in competitive exams and aptitude sections.

Question 3

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 ar…

Accepted Answer

Step 1: Convert walking speeds to m/s Speed of first person = 4.5 km/hr = (4.5 × 5) / 18 = 1.25 m/s Speed of second person = 5.4 km/hr = (5.4 × 5) / 18 = 1.5 m/s Step 2: Let the length of the train be L meters We know: 
Time = Distance / Relative Speed
So, L / (Train Speed - Person Speed) = Time
 Use the first case (Person walking at 1.25 m/s): 
L / (V - 1.25) = 8.4  → (1)
 Use the second case (Person walking at 1.5 m/s): 
L / (V - 1.5) = 8.5  → (2)
 Step 3: Solve the two equations From (1): L = 8.4 × (V - 1.25) From (2): L = 8.5 × (V - 1.5) Equating both expressions for L: 
8.4(V - 1.25) = 8.5(V - 1.5)
 Expand both sides: 
8.4V - 10.5 = 8.5V - 12.75
 Bring all terms to one side: 
8.5V - 8.4V = 12.75 - 10.5
0.1V = 2.25
⇒ V = 2.25 / 0.1 = 22.5 m/s
 Step 4: Convert train speed to km/h 
22.5 m/s = 22.5 × 18 / 5 = 81 km/h
 Answer: The speed of the train is 81 km/h. This type of problem uses the concept of relative speed and distance = speed × time. It’s a common question in aptitude tests, and mastering it builds speed and accuracy for competitive exams.

Question 4

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

Accepted Answer

Step 1: Understand the setup Speed of fast train = 40 km/hr Speed of slower train = 20 km/hr The man is sitting in the slower train, so his speed is also 20 km/hr Time taken to completely pass the man = 5 seconds Step 2: Calculate relative speed 
Relative speed = Speed of fast train - Speed of man
               = 40 - 20 = 20 km/hr
               = (20 × 1000) / 3600 = 5.56 m/s
 Step 3: Use time and speed to calculate length of the train 
Length = Relative speed × Time
       = 5.56 m/s × 5 s
       = 27.78 meters
 Answer: The length of the fast train is approximately 27.78 meters. This problem involves converting units and applying the basic distance = speed × time formula. Since both trains are moving in the same direction, we use the relative speed (difference in speeds). Questions like this are common in quantitative aptitude exams and help build understanding of relative motion.

Question 5

A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

Accepted Answer

Step 1: Understand the given data Time taken to pass a telegraph post = 8 seconds Time taken to pass a bridge = 20 seconds Length of the bridge = 264 meters Step 2: Let the length of the train be L meters When the train passes the telegraph post, it covers its own length in 8 seconds So, L = Speed × 8 → Speed = L / 8 Step 3: When it passes the bridge Total distance covered = Length of train + Length of bridge = L + 264 Time taken = 20 seconds So, (L + 264) = Speed × 20 = (L / 8) × 20 Step 4: Solve the equation 
L + 264 = (L / 8) × 20
L + 264 = (20L) / 8
L + 264 = (5L) / 2

Multiply both sides by 2:
2L + 528 = 5L
528 = 5L - 2L
528 = 3L
L = 176 meters
 Step 5: Find the speed of the train 
Speed = L / 8 = 176 / 8 = 22 m/s
Convert to km/hr: 22 × 18 / 5 = 79.2 km/hr
 Answer: The speed of the train is 79.2 km/hr This is a classic speed–distance–time problem where the trick is to understand that when a train crosses a point (like a pole), it covers its own length, and when it crosses a bridge, it covers its own length plus the bridge length. Problems like this test your algebraic setup and unit conversion skills.

Question 6

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

Accepted Answer

Step 1: Understand the problem The train passes a pole in 15 seconds. The train passes a platform of 100 meters in 25 seconds. We need to find the length of the train. Step 2: Find the speed of the train When a train passes a pole, it covers a distance equal to its own length. Let the length of the train be L meters. Speed of the train = L / 15 (in m/s) Step 3: Use platform data to form an equation When the train passes a platform, it covers (Length of train + Length of platform). Time taken = 25 seconds Total distance = L + 100 Speed = (L + 100) / 25 Step 4: Equating both expressions for speed 
L / 15 = (L + 100) / 25

Cross-multiply:
25L = 15(L + 100)
25L = 15L + 1500
25L - 15L = 1500
10L = 1500
L = 150
 Answer: The length of the train is 150 meters. This problem highlights how to apply the distance = speed × time formula in scenarios where a moving object (train) crosses a stationary object (pole or platform). The key is to set up the equations correctly and solve for the unknown.

Question 7

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

Accepted Answer

Step 1: Understand the problem The train is 300 meters long. It takes 18 seconds to pass a signal pole. It takes 39 seconds to cross a platform. We need to find the length of the platform. Step 2: Calculate the speed of the train When a train crosses a signal pole, it covers a distance equal to its own length. Speed = Distance / Time = 300 / 18 = 16.67 m/s Step 3: Use speed to find platform length When a train crosses a platform, it covers its own length + length of platform. Total time to cross platform = 39 seconds Distance = Speed × Time = 16.67 × 39 = 650.13 meters Distance includes 300 meters of train + platform length Platform length = 650.13 - 300 = 350.13 meters Answer: The length of the platform is approximately 350 meters. This problem demonstrates how to calculate distance using the formula distance = speed × time. Knowing how long the train takes to cross a pole helps us calculate its speed, which we can then use to determine how long a platform is when the total time is known.

Question 8

A train travelling at a speed of 75 mph enters a tunnel 3½ miles long. The train is ¼ mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

Accepted Answer

Step 1: Understand the problem Speed of the train = 75 mph Length of the tunnel = 3.5 miles Length of the train = 0.25 miles To completely pass the tunnel, the train must cover: 3.5 + 0.25 = 3.75 miles Step 2: Use the formula: Time = Distance / Speed 
Total distance to be covered = 3.75 miles  
Speed = 75 miles/hour  

Time = 3.75 / 75 = 0.05 hours
 Step 3: Convert time to minutes 
0.05 hours × 60 minutes/hour = 3 minutes
 Answer: The train takes 3 minutes to pass completely through the tunnel. This question checks your understanding of relative distance when a train passes completely through a tunnel. The key idea is that the train must travel a distance equal to its own length plus the length of the tunnel. Converting units between miles, hours, and minutes is crucial for such real-life application problems.

Question 9

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:

Accepted Answer

Let the speed of each train be x m/s. Since the trains are moving in opposite directions, their relative speed is 2x. Total length to be crossed = length of train 1 + length of train 2 = 120 + 120 = 240 meters. Using the formula: Distance = Speed × Time240 = 2x × 12=> x = 10 m/s Convert the speed to km/hr: 1 m/s = 18/5 km/hr=> 10 m/s = 10 × (18/5) = 36 km/hr Hence, the speed of each train is 36 km/hr.

Question 10

A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

Accepted Answer

We are given the following: Length of the first train = 270 m Speed of the first train = 120 km/h Speed of the second train = 80 km/h Time taken to cross = 9 seconds We need to find: Length of the second train Step 1: Convert the combined speed into meters per second When two trains move in opposite directions, their relative speed = sum of their speeds.
Relative Speed = 120 + 80 = 200 km/h
To convert km/h to m/s, multiply by (1000 / 3600):
=> 200 × (1000 / 3600) = 55.56 m/s
 Step 2: Use the speed-distance-time formula Distance = Speed × Time
Total distance covered in 9 seconds = 55.56 × 9 = 500.04 meters
 Step 3: Understand what distance is covered The total distance covered while crossing = length of first train + length of second train
Let the length of the second train = x meters
Then, 270 + x = 500.04
=> x = 500.04 - 270 = 230.04 meters
 Final Answer: The length of the other train is approximately 230 meters

Question 11

Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

Accepted Answer

We are given: Speed of Train 1 = 60 km/h Speed of Train 2 = 90 km/h Length of Train 1 = 1.10 km = 1100 m Length of Train 2 = 0.90 km = 900 m Step 1: Calculate total distance to be covered Both trains are moving in opposite directions, so they will cross each other completely.Total distance = Length of Train 1 + Length of Train 2= 1100 + 900 = 2000 meters Step 2: Convert relative speed to m/s Relative Speed = 60 + 90 = 150 km/hConvert to m/s: 150 × (1000 / 3600) = 41.67 m/s Step 3: Calculate time using the formula Time = Distance / Speed= 2000 / 41.67 ≈ 48 seconds Final Answer: The time taken by the slower train to cross the faster train is approximately 48 seconds

Question 12

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

Accepted Answer

We are given: Time taken by Train A to cross a post = 10 seconds Time taken by Train B to cross a post = 15 seconds Length of each train = 120 meters Step 1: Find speed of each train Speed = Distance / TimeSpeed of Train A = 120 / 10 = 12 m/sSpeed of Train B = 120 / 15 = 8 m/s Step 2: Find relative speed when moving in opposite directions Relative Speed = 12 + 8 = 20 m/sCombined length = 120 + 120 = 240 meters Step 3: Calculate time to cross each other Time = Distance / Speed= 240 / 20 = 12 seconds Final Answer: They will cross each other in 12 seconds

Question 13

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 ar…

Accepted Answer

We are given: Person A walks at 4.5 km/h and is overtaken in 8.4 seconds Person B walks at 5.4 km/h and is overtaken in 8.5 seconds Both persons walk in the same direction as the train Let the speed of the train be x km/h Step 1: Use the relative speed concept Train length (L) = Relative speed × TimeFor person A:L = (x - 4.5) × (5 / 18) × 8.4For person B:L = (x - 5.4) × (5 / 18) × 8.5 Step 2: Set both expressions equal (since train length is same) (x - 4.5) × 8.4 = (x - 5.4) × 8.5 Step 3: Solve the equation 8.4x - 37.8 = 8.5x - 45.9=> 45.9 - 37.8 = 8.5x - 8.4x=> 8.1 = 0.1x=> x = 81 km/hr Final Answer: The speed of the train is 81 km/hr

Question 14

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

Accepted Answer

We are given: Length of train = 240 m Time to pass a pole = 24 seconds Length of platform = 650 m Step 1: Find speed of the train Speed = Distance / Time= 240 / 24 = 10 m/s Step 2: Calculate total distance to pass the platform Total distance = train length + platform length= 240 + 650 = 890 m Step 3: Calculate time to pass the platform Time = Distance / Speed= 890 / 10 = 89 seconds Final Answer: The train will take 89 seconds to pass the platform.

Question 15

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:

Accepted Answer

We are given: Train A reaches its destination 9 hours after meeting Train B reaches its destination 16 hours after meeting Concept:Let the two trains meet at point M.After meeting, the time taken to reach their destinations is inversely proportional to their speeds. Step 1: Use inverse time-speed relationshipSpeed of Train A / Speed of Train B = √(16) / √(9)= 4 / 3 Final Answer:The ratio of their speeds is 4:3

Question 16

Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

Accepted Answer

We are given: Speed of Train A = 60 km/h Speed of Train B = 90 km/h Length of Train A = 1.10 km = 1100 m Length of Train B = 0.90 km = 900 m Step 1: Find total distance to be coveredTotal length = 1100 + 900 = 2000 meters Step 2: Find relative speedRelative Speed = 60 + 90 = 150 km/hConvert to m/s: 150 × (1000 / 3600) = 41.67 m/s Step 3: Calculate time takenTime = Distance / Speed= 2000 / 41.67 = 48 seconds Final Answer:The time taken by the slower train to cross the faster one is 48 seconds

Question 17

Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

Accepted Answer

We are given: Length of each train = 100 m Time to cross each other = 8 seconds One train is twice as fast as the other Step 1: Let the slower train's speed be x m/sThen the faster train's speed = 2x m/sRelative speed = x + 2x = 3x Step 2: Use distance = speed × timeTotal distance = 100 + 100 = 200 m3x × 8 = 200 → x = 25 / 3 ≈ 8.33 m/s Step 3: Convert faster train's speed to km/hr2x = 2 × 8.33 ≈ 16.66 m/s= 16.66 × (18/5) ≈ 60 km/hr Final Answer:The speed of the faster train is 60 km/hr

Question 18

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

Accepted Answer

We are given: Length of Train A = 140 m Length of Train B = 160 m Speed of Train A = 60 km/h Speed of Train B = 40 km/h Step 1: Find total distance to be coveredTotal length = 140 + 160 = 300 meters Step 2: Calculate relative speedRelative Speed = 60 + 40 = 100 km/hConvert to m/s: 100 × (1000 / 3600) = 27.78 m/s Step 3: Use time = distance / speedTime = 300 / 27.78 ≈ 10.8 seconds Final Answer:The time taken to cross each other is 10.8 seconds

Question 19

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?

Accepted Answer

We are given: Distance between stations A and B = 110 km Train A starts at 7 a.m. at 20 km/h Train B starts at 8 a.m. at 25 km/h Step 1: Distance covered by Train A before Train B startsFrom 7 a.m. to 8 a.m., Train A travels = 20 × 1 = 20 kmRemaining distance = 110 – 20 = 90 km Step 2: Relative speed after 8 a.m.Relative speed = 20 + 25 = 45 km/h Step 3: Time taken to meetTime = 90 / 45 = 2 hours Final Answer:They meet at 8 a.m. + 2 hours = 10 a.m.

Question 20

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

Accepted Answer

We are given: Length of train = 300 m Time to cross platform = 39 sec Time to cross signal pole = 18 sec Step 1: Calculate train speedSpeed = Distance / Time= 300 / 18 = 16.67 m/s Step 2: Distance covered when crossing platform= Speed × Time = 16.67 × 39 = 650 m Step 3: Subtract train length to find platform lengthPlatform length = 650 – 300 = 350 meters

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