Question 1

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

Accepted Answer

Step 1: Convert the speed of the first train to m/s 
Speed = 50 km/hr = (50 × 1000) / 3600 = 13.89 m/s
 Step 2: Let the speed of the second train be x km/hr 
Then, speed in m/s = (x × 1000) / 3600 = x × (5/18) m/s
 Step 3: Total length to be covered when trains cross each other = 108 + 112 = 220 m Relative speed = 13.89 + (5x/18) m/s Time = Distance / Relative Speed 
6 = 220 / (13.89 + (5x/18))
 Step 4: Solve the equation 
13.89 + (5x / 18) = 220 / 6 = 36.67

(5x / 18) = 36.67 - 13.89 = 22.78

Multiply both sides by 18:
5x = 410.04
x = 410.04 / 5 = 82.01
 Answer: 82 km/hr The speed of the second train is approximately 82 km/hr. This is a classic time–distance–speed problem involving relative speed when two objects move towards each other. Such problems are common in quantitative aptitude sections of exams like SSC, Bank PO, and Railway Recruitment.

Question 2

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

Accepted Answer

Step 1: Let the length of the first train be L meters Speed of first train = 48 km/h = (48 × 1000) / 3600 = 13.33 m/s Speed of second train = 42 km/h = (42 × 1000) / 3600 = 11.67 m/s Step 2: Total relative speed = 13.33 + 11.67 = 25 m/s Time to cross each other = 12 seconds 
Distance = Speed × Time = 25 × 12 = 300 meters
 Step 3: Let the second train’s length be L/2 
L + (L/2) = 300
(3L/2) = 300 ⇒ L = 200 meters
 Step 4: Now use platform crossing time Total time to cross the platform = 45 seconds Speed = 13.33 m/s, Length of train = 200 meters 
Distance = Speed × Time = 13.33 × 45 = 599.85 ≈ 600 meters
 Length of platform = 600 - 200 = 400 meters Answer: 400 meters The length of the platform is 400 meters. This question tests your understanding of speed, distance, and time with relative motion. It is common in competitive exams, and understanding how to separate the distances covered in different parts (with another train vs a platform) is key to solving it.

Question 3

Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

Accepted Answer

Step 1: Understand the setup Length of each train = 500 meters Speeds: Train A (faster) = 45 km/h Train B (slower) = 30 km/h They are moving in opposite directions on parallel tracks. Step 2: Convert speeds to meters per second 
Speed of Train A = 45 × (1000 / 3600) = 12.5 m/s
Speed of Train B = 30 × (1000 / 3600) = 8.33 m/s
 Step 3: Relative speed when moving in opposite directions = 12.5 + 8.33 = 20.83 m/s Step 4: Since we want the slower train to pass the driver of the faster train Only the length of the slower train (Train B) = 500 m needs to cross the driver of Train A. 
Time = Distance / Relative Speed
     = 500 / 20.83 ≈ 24 seconds
 Answer: 24 seconds The slower train will take approximately 24 seconds to pass the driver of the faster train. This question is based on relative motion where two trains move in opposite directions. Understanding how to isolate the relevant length and apply the relative speed concept is key in such problems. Perfect for candidates preparing for competitive exams.

Question 4

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

Accepted Answer

Step 1: Let the lengths of the two trains be L₁ and L₂, and their speeds be S₁ and S₂. Train 1 crosses a man in 27 seconds ⇒ L₁ = S₁ × 27 Train 2 crosses a man in 17 seconds ⇒ L₂ = S₂ × 17 Step 2: The two trains cross each other in 23 seconds when moving in opposite directions. That means: 
L₁ + L₂ = (S₁ + S₂) × 23
 Step 3: Substitute L₁ and L₂ 
S₁ × 27 + S₂ × 17 = (S₁ + S₂) × 23
 Step 4: Expand and simplify the equation 
27S₁ + 17S₂ = 23S₁ + 23S₂
=> 27S₁ - 23S₁ = 23S₂ - 17S₂
=> 4S₁ = 6S₂
=> S₁ / S₂ = 6 / 4 = 3 / 2
 Answer: 3 : 2 The ratio of their speeds is 3:2. This is a classic relative motion problem involving trains. It uses the concept of time = distance/speed, and setting up linear equations from the conditions provided. This type of question is commonly asked in competitive exams like SSC, Railway, and Banking.

Question 5

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

Accepted Answer

Step 1: Let the speed of the train be S km/hr and the length of the train be L meters. Person A is walking at 2 km/hr and is overtaken in 9 seconds. Person B is walking at 4 km/hr and is overtaken in 10 seconds. Step 2: Convert speeds to m/s 
1 km/hr = 5/18 m/s

Relative speed while overtaking Person A = (S - 2) × 5/18 m/s
Relative speed while overtaking Person B = (S - 4) × 5/18 m/s
 Step 3: Use time = distance / speed 
L = (S - 2) × 5/18 × 9        ...[Equation 1]
L = (S - 4) × 5/18 × 10       ...[Equation 2]
 Step 4: Equating both expressions for L 
(S - 2) × 5 × 9 = (S - 4) × 5 × 10
=> (S - 2) × 9 = (S - 4) × 10
=> 9S - 18 = 10S - 40
=> 40 - 18 = 10S - 9S
=> 22 = S
 Step 5: Find the length of the train 
L = (S - 2) × 5/18 × 9
=> L = (22 - 2) × 5/18 × 9
=> L = 20 × 5 × 0.5 = 50 meters
 Answer: 50 meters The length of the train is 50 meters. This problem is based on the concept of relative speed and time-distance conversion. The key is to account for the direction of motion and use the appropriate conversion factor from km/hr to m/s. These types of questions are common in quantitative aptitude exams.

Question 6

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

Step 1: Let the speed of the slower train be x m/s. Then the speed of the faster train = 2x m/s. Step 2: Both trains are 100 m long and are moving in opposite directions. Total distance to be covered while crossing = 100 + 100 = 200 meters Step 3: Relative speed when moving in opposite directions = x + 2x = 3x m/s Time taken to cross = 8 seconds Step 4: Apply the formula: distance = speed × time 
200 = 3x × 8
=> 3x = 200 / 8 = 25
=> x = 25 / 3 ≈ 8.33 m/s
 Step 5: Speed of the faster train = 2x = 2 × 25/3 = 50/3 m/s Convert to km/hr: (multiply by 18/5) 
Speed = (50/3) × (18/5) = 60 km/hr
 Answer: 60 km/hr The speed of the faster train is 60 km/hr. This is a classic problem involving relative speed when two objects move in opposite directions. The key is to correctly account for their combined length and use the correct conversion factor between m/s and km/hr.

Question 7

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

Step 1: Find the speed of the train The train passes a pole in 24 seconds. When a train passes a pole, it covers a distance equal to its own length. 
Length of train = 240 m
Time = 24 seconds
Speed = Distance / Time = 240 / 24 = 10 m/s
 Step 2: Total distance to cover while crossing a platform When the train crosses a platform, it covers the distance equal to its own length + length of the platform. 
Length of platform = 650 m
Total distance = 240 + 650 = 890 m
 Step 3: Time taken to cross the platform 
Speed = 10 m/s
Time = Distance / Speed = 890 / 10 = 89 seconds
 Answer: 89 seconds The train will take 89 seconds to cross the platform. This type of question helps in understanding the concept of relative motion and how different lengths and times relate when a moving object passes a stationary object or structure like a platform.

Question 8

A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

Accepted Answer

Step 1: Convert speeds from km/h to m/s 
Speed of train = 45 km/h = (45 × 1000) / 3600 = 12.5 m/s
Speed of jogger = 9 km/h = (9 × 1000) / 3600 = 2.5 m/s
 Step 2: Find the relative speed Since both are moving in the same direction, subtract the jogger’s speed from the train’s speed. 
Relative speed = 12.5 - 2.5 = 10 m/s
 Step 3: Total distance to be covered to completely pass the jogger The jogger is 240 meters ahead, and the train is 120 meters long. So, the train has to cover: 
Distance = 240 + 120 = 360 meters
 Step 4: Time to pass the jogger 
Time = Distance / Relative Speed = 360 / 10 = 36 seconds
 Answer: 36 seconds The train will take 36 seconds to pass the jogger completely. This is a classic example of a relative speed problem where both the train and the person are moving in the same direction. Understanding relative motion is crucial for solving such questions accurately in time-based aptitude exams.

Question 9

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

Step 1: Understand the given data Length of each train = 120 meters Time taken by first train to cross a pole = 10 seconds Time taken by second train to cross a pole = 15 seconds Step 2: Calculate the speed of each train Speed = Distance / Time 
Speed of Train A = 120 / 10 = 12 m/s
Speed of Train B = 120 / 15 = 8 m/s
 Step 3: Find the relative speed Since the trains are moving in opposite directions, their relative speeds will be added: 
Relative speed = 12 + 8 = 20 m/s
 Step 4: Total distance to be covered when trains cross each other Each train is 120 m long, so total distance = 120 + 120 = 240 meters Step 5: Calculate the time to cross each other 
Time = Total Distance / Relative Speed = 240 / 20 = 12 seconds
 Answer: 12 seconds The two trains will cross each other in 12 seconds when moving in opposite directions. This question demonstrates how the concept of relative speed applies when two moving bodies travel toward each other. It’s a commonly tested topic in time-speed-distance problems found in competitive exams.

Question 10

A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

Accepted Answer

Step 1: Understand the given data Length of the train = 110 meters Speed of the train = 60 km/h Speed of the man = 6 km/h The man is running in the opposite direction of the train Step 2: Convert speeds to m/s To convert km/h to m/s, multiply by 5/18 
Speed of train = 60 × (5/18) = 16.67 m/s
Speed of man = 6 × (5/18) = 1.67 m/s
 Step 3: Calculate relative speed Since they are moving in opposite directions, relative speed = sum of their speeds 
Relative speed = 16.67 + 1.67 = 18.34 m/s
 Step 4: Calculate time taken to pass the man 
Time = Distance / Speed = 110 / 18.34 ≈ 6 seconds
 Answer: 6 seconds The train will pass the man in approximately 6 seconds. This problem illustrates the importance of converting units correctly and applying the concept of relative speed when two objects are moving toward or away from each other.

Question 11

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

Accepted Answer

Step 1: Understand the given data Length of the train = 130 meters Speed of the train = 45 km/h Time taken to cross the bridge = 30 seconds Step 2: Convert speed to m/s To convert km/h to m/s, multiply by 5/18: 
Speed = 45 × (5/18) = 12.5 m/s
 Step 3: Calculate total distance covered in 30 seconds 
Distance = Speed × Time = 12.5 × 30 = 375 meters
 Step 4: Calculate the length of the bridge Total distance covered = Length of train + Length of bridge 
375 = 130 + Length of bridge
Length of bridge = 375 - 130 = 245 meters
 Answer: 245 meters The train will cross a bridge of 245 meters in 30 seconds. This question demonstrates the use of basic speed–distance–time formula, and how the total distance covered when a train crosses a bridge includes both the train's length and the bridge's length.

Question 12

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

Accepted Answer

Step 1: Understand the given data Speed of the goods train = 72 km/h Length of the platform = 250 meters Time taken to cross the platform = 26 seconds Step 2: Convert speed to meters/second 
Speed in m/s = 72 × (5/18) = 20 m/s
 Step 3: Calculate total distance covered in 26 seconds 
Distance = Speed × Time = 20 × 26 = 520 meters
 Step 4: Find the length of the train Total distance covered includes the train and the platform: 
Length of train = Total distance - Length of platform
Length of train = 520 - 250 = 270 meters
 Answer: 270 meters The length of the goods train is 270 meters. This problem illustrates a key concept in speed and distance calculations, where the total distance covered by the train while crossing a platform is the sum of its own length and the length of the platform.

Question 13

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?

Accepted Answer

Step 1: Understand the given data Time taken to pass the platform = 36 seconds Time taken to pass a man = 20 seconds Speed of the train = 54 km/h Step 2: Convert speed to meters per second 
Speed = 54 × (5 / 18) = 15 m/s
 Step 3: Calculate length of the train 
Length of train = Speed × Time to pass man
                = 15 × 20 = 300 meters
 Step 4: Calculate total distance to pass the platform 
Distance = Speed × Time to pass platform
         = 15 × 36 = 540 meters
 Step 5: Calculate the length of the platform 
Length of platform = Total distance - Length of train
                   = 540 - 300 = 240 meters
 Answer: 240 meters The length of the platform is 240 meters. This question tests your ability to apply the formula Distance = Speed × Time in multiple contexts. By first finding the train’s length (using the time to pass a standing man), and then using the total time to pass a platform, we deduce the platform’s length. This type of question is common in competitive exams and helps strengthen concepts in speed, time, and distance.

Question 14

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:

Accepted Answer

Step 1: Understand the given data Both trains are of equal length Speed of faster train = 46 km/hr Speed of slower train = 36 km/hr Time taken to overtake = 36 seconds Step 2: Convert speeds to meters per second 
Speed of faster train = 46 × (5 / 18) = 12.78 m/s
Speed of slower train = 36 × (5 / 18) = 10.00 m/s
 Step 3: Find the relative speed (since both are moving in the same direction) 
Relative speed = 12.78 - 10.00 = 2.78 m/s
 Step 4: Total distance covered in overtaking To overtake, the faster train must cover the length of both trains (since both are of equal length): 
Let the length of each train be L meters. 
Then total distance = 2L
 Step 5: Use the formula Distance = Speed × Time 
2L = 2.78 × 36
2L = 100.08
L = 50.04
 Answer: 50 meters The length of each train is 50 meters. This is a classic problem in speed-time-distance where two objects move in the same direction. The relative speed is crucial here because the faster train is gaining on the slower one. We also consider the full length of both trains since complete overtaking involves clearing both ends.

Question 15

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

Step 1: Understand the given information Distance between stations A and B = 110 km Train 1 starts from A at 7 a.m. with a speed of 20 kmph Train 2 starts from B at 8 a.m. with a speed of 25 kmph Step 2: Calculate the head start of Train 1 
Between 7 a.m. and 8 a.m., Train 1 travels for 1 hour at 20 kmph. 
Distance covered by Train 1 in 1 hour = 20 km
 Step 3: Remaining distance between the trains at 8 a.m. 
Remaining distance = 110 - 20 = 90 km
 Step 4: Use relative speed to find meeting time 
From 8 a.m., both trains are moving towards each other. 
Combined speed = 20 kmph + 25 kmph = 45 kmph
Time to meet = Distance / Relative speed = 90 / 45 = 2 hours
 Step 5: Add the time to 8 a.m. 
8 a.m. + 2 hours = 10 a.m.
 Answer: 10:00 a.m. The two trains will meet at 10:00 a.m.. This is a classic relative speed problem involving two trains starting at different times. The key is to account for the early start of the first train and then apply the concept of relative speed when both are moving towards each other. This approach is commonly tested in aptitude and entrance exams.

Question 16

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:

Accepted Answer

Step 1: Understand the given information Length of the train = 125 meters Speed of the man = 5 km/h The train passes the man in 10 seconds Both are moving in the same direction Step 2: Use relative speed concept Since the train and the man are moving in the same direction, we subtract the man's speed from the train's speed to get the relative speed. 
Let the speed of the train be x km/h. 
Relative speed = (x - 5) km/h = ((x - 5) × 1000) / 3600 m/s
 Step 3: Use the formula: Distance = Speed × Time 
Distance = 125 meters 
Time = 10 seconds 
Speed = Distance / Time = 125 / 10 = 12.5 m/s
 Step 4: Solve for x 
(x - 5) × 1000 / 3600 = 12.5 
(x - 5) = (12.5 × 3600) / 1000 
(x - 5) = 45 
x = 50 km/h
 Answer: 50 km/h The speed of the train is 50 kilometers per hour. This problem tests the understanding of relative speed in the same direction. Since the man and the train move in the same direction, the train takes longer to overtake him, and the effective speed is reduced. The use of basic distance = speed × time formula allows solving such problems efficiently.

Question 17

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

Accepted Answer

Step 1: Understand the given information Speed of the train = 60 km/h Time taken to cross a pole = 9 seconds When a train crosses a pole, it covers a distance equal to its own length. Step 2: Convert the speed to meters per second 
1 km/h = 5/18 m/s 
So, 60 km/h = 60 × 5/18 = 16.67 m/s
 Step 3: Use the formula: Distance = Speed × Time 
Distance = 16.67 × 9 = 150 meters
 Answer: 150 meters The length of the train is 150 meters. This problem checks the basic application of speed, distance, and time formula. When a train crosses a pole, it travels a distance equal to its length. Converting speed into meters per second is essential to match units and compute accurately.

Question 18

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?

Accepted Answer

Step 1: Understand the given information Length of train = 360 meters Length of bridge = 140 meters Total distance to cover = 360 + 140 = 500 meters Speed of train = 45 km/hr Step 2: Convert the speed to meters per second 
1 km/h = 5/18 m/s 
So, 45 km/h = 45 × 5/18 = 12.5 m/s
 Step 3: Use the formula: Time = Distance / Speed 
Time = 500 / 12.5 = 40 seconds
 Answer: 40 seconds The train will take 40 seconds to cross the bridge completely. This question involves the concept of relative motion where the train has to cover both its own length and the bridge’s length. Converting the speed into m/s ensures unit consistency while applying the distance-speed-time formula.

Question 19

A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

Accepted Answer

Step 1: Understand the given data Length of train = 800 meters Speed of train = 78 km/hr Time to cross the tunnel = 1 minute = 60 seconds Step 2: Convert speed to meters per second 
Speed in m/s = 78 × (5/18) = 21.67 m/s
 Step 3: Use the formula: Distance = Speed × Time 
Total distance covered in 60 seconds = 21.67 × 60 = 1300 meters
 Step 4: Calculate the length of the tunnel 
Distance = Length of train + Length of tunnel 
1300 = 800 + Length of tunnel 
Length of tunnel = 1300 - 800 = 500 meters
 Answer: 500 meters The length of the tunnel is 500 meters. This problem demonstrates the use of basic motion formulas where a train covers its own length plus the length of the tunnel in the given time. Converting the train’s speed to m/s ensures consistency in units for calculating distance accurately.

Question 20

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

Step 1: Understand the scenario Two trains start at the same time from Howrah and Patna towards each other. They meet at some point. After meeting: Train A (from Howrah) takes 9 hours to reach Patna. Train B (from Patna) takes 16 hours to reach Howrah. Step 2: Use the concept of inverse time-speed relationship When two objects move toward each other and meet, the distances left after meeting are inversely proportional to their speeds. 
So, Speed of Train A : Speed of Train B = √(1 / 9) : √(1 / 16)
                                   = 1/3 : 1/4
                                   = 4 : 3
 Answer: 4 : 3 The ratio of their speeds is 4:3. This classic problem is solved using the concept that the time taken to complete the remaining journey after meeting is inversely proportional to the speed of the trains. Such problems are commonly asked in aptitude exams to test conceptual clarity on relative speed and ratios.

Problems on Trains Questions