Question 1

Train A of length 150 m crosses a stationary platform in 15 seconds. What is the speed of Train A in km/h?

Accepted Answer

Step 1: When a train crosses a platform, it travels a distance equal to its own length. Distance = 150 m, Time = 15 seconds. Step 2: Speed = Distance ÷ Time = 150 ÷ 15 = 10 m/s. Step 3: Convert m/s to km/h by multiplying by 3.6: 10 × 3.6 = 36 km/h.

Question 2

A train travels a distance of 360 km in 4 hours. What is the speed of the train in metres per second?

Accepted Answer

Step 1: Speed in km/h = 360 ÷ 4 = 90 km/h. Step 2: Convert to m/s using the formula: speed (m/s) = speed (km/h) × (5/18). Step 3: 90 × (5/18) = 450/18 = 25 m/s. Therefore, the answer is 25 m/s.

Question 3

Train A of length 150 m crosses a stationary platform in 15 seconds. What is the speed of Train A in km/h?

Accepted Answer

Step 1: The train crosses the platform means it travels a distance equal to its own length. Distance = 150 m, Time = 15 seconds. Step 2: Speed in m/s = Distance ÷ Time = 150 ÷ 15 = 10 m/s. Step 3: Convert to km/h by multiplying by 3.6 (or 18/5): 10 × 3.6 = 36 km/h.

Question 4

Train A and Train B start simultaneously from stations P and Q respectively, which are 480 km apart. Train A travels towards Q at 60 km/h, while Train B travels towards P at 40 km/h. After how many hours will the two trains meet, and at what distance from station P will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = sum of individual speeds = 60 + 40 = 100 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 480 ÷ 100 = 4.8 hours. Step 3: Distance from P = Speed of Train A × Time = 60 × 4.8 = 288 km. Therefore, the trains meet after 4.8 hours at 288 km from station P.

Question 5

Train A and Train B start simultaneously from opposite ends of a 360 km track. Train A travels at 80 km/h and Train B travels at 100 km/h. After how many hours will they meet each other?

Accepted Answer

Step 1: When two trains travel towards each other from opposite ends, their relative speed = Sum of individual speeds = 80 + 100 = 180 km/h. Step 2: Distance to be covered = 360 km. Step 3: Using formula: Time = Distance / Relative Speed = 360 / 180 = 2 hours. Therefore, the trains will meet after 2 hours.

Question 6

Two trains, A and B, start simultaneously from stations X and Y respectively, which are 480 km apart. Train A travels towards Y at 60 km/h, while train B travels towards X at 40 km/h. After how many hours will they meet, and at what distance from station X?

Accepted Answer

Step 1: When two trains travel towards each other, their relative speed = 60 + 40 = 100 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 480 ÷ 100 = 4.8 hours. Step 3: Distance from X where they meet = Speed of A × Time = 60 × 4.8 = 288 km. Therefore, they meet after 4.8 hours at 288 km from station X.

Question 7

Two trains, A and B, start simultaneously from stations X and Y respectively, which are 480 km apart. Train A travels towards Y at 60 km/h, while train B travels towards X at 40 km/h. After they meet, train A takes 6 hours to reach Y, while train B takes 10 hours to reach X. If both trains had started 2 hours later, by what time (in hours after the original start time) would they meet?

Accepted Answer

Step 1: Find the meeting point. Let meeting time = t hours. Distance covered by A = 60t, Distance covered by B = 40t. Since 60t + 40t = 480, we get 100t = 480, so t = 4.8 hours. Step 2: Verify consistency. After meeting at 4.8 hours, train A covers remaining distance in 6 hours at 60 km/h = 360 km. Train B covers remaining distance in 10 hours at 40 km/h = 400 km. Total = 360 + 400 = 760 km ≠ 480 km. This indicates the problem statement contains a consistency check (the given times after meeting are red herrings). Step 3: The actual meeting time depends only on speeds and initial distance. If both start 2 hours later, they still meet after 4.8 hours of travel, which is 2 + 4.8 = 6.8 hours after the original start time.

Question 8

Two trains A and B start simultaneously from stations P and Q respectively towards each other. The distance between P and Q is 560 km. Train A travels at 80 km/h and Train B travels at 60 km/h. After how many hours will they meet, and how far from station P will the meeting point be?

Accepted Answer

Step 1: Relative speed when moving towards each other = 80 + 60 = 140 km/h. Step 2: Time to meet = 560 ÷ 140 = 4 hours. Step 3: Distance covered by Train A (from P) = 80 × 4 = 320 km. Therefore, they meet 320 km from station P after 4 hours.

Question 9

Two trains are moving towards each other on parallel tracks. Train X travels at 60 km/h and Train Y travels at 40 km/h. If they are 500 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two trains move towards each other, their relative speed = Speed of Train X + Speed of Train Y = 60 + 40 = 100 km/h. Step 2: Time to meet = Distance ÷ Relative Speed = 500 ÷ 100 = 5 hours.

Question 10

Train A and Train B start from the same station at the same time. Train A travels at 72 km/h and Train B travels at 54 km/h in the same direction. After how much time will Train A be 9 km ahead of Train B?

Accepted Answer

Step 1: Relative speed = 72 - 54 = 18 km/h (since both travel in same direction). Step 2: Distance to be covered = 9 km. Step 3: Time = Distance ÷ Relative speed = 9 ÷ 18 = 0.5 hours = 30 minutes.

Question 11

A train of length 180 m passes a stationary pole in 9 seconds. How long will it take to pass another train of length 120 m moving in the same direction at 10 m/s?

Accepted Answer

Step 1: Find speed of first train. When passing a pole, distance = train length = 180 m. Speed = 180 ÷ 9 = 20 m/s. Step 2: Since both trains move in same direction, relative speed = 20 - 10 = 10 m/s. Step 3: Total distance to cover = 180 + 120 = 300 m. Step 4: Time = 300 ÷ 10 = 30 seconds.

Question 12

Train A is 150 m long and travels at 45 km/h. How long will it take to completely cross a platform that is 250 m long?

Accepted Answer

Step 1: When a train crosses a platform, the total distance to cover = length of train + length of platform = 150 + 250 = 400 m. Step 2: Convert speed to m/s: 45 km/h = 45 × (5/18) = 12.5 m/s. Step 3: Time = Distance ÷ Speed = 400 ÷ 12.5 = 32 seconds.

Question 13

Two trains are moving towards each other on parallel tracks. Train X has a speed of 60 km/h and Train Y has a speed of 40 km/h. If they are 500 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two trains move towards each other, their relative speed = Sum of their individual speeds = 60 + 40 = 100 km/h. Step 2: Time to meet = Distance ÷ Relative Speed = 500 ÷ 100 = 5 hours.

Question 14

A train 180 metres long is running at 45 km/h. How long will it take to pass a platform that is 270 metres long?

Accepted Answer

Step 1: For a train to completely pass a platform, the distance covered = Length of train + Length of platform = 180 + 270 = 450 metres. Step 2: Speed = 45 km/h = 45 × 5/18 = 12.5 m/s. Step 3: Time = Distance ÷ Speed = 450 ÷ 12.5 = 36 seconds.

Question 15

A train is 300 metres long and is running at a speed of 90 km/h. How much time (in seconds) will it take to cross a pole?

Accepted Answer

Step 1: Convert speed from km/h to m/s. Speed = 90 × (5/18) = 25 m/s. Step 2: To cross a pole, the train must cover a distance equal to its own length = 300 m. Step 3: Time = Distance ÷ Speed = 300 ÷ 25 = 12 seconds. Therefore, the answer is 12 seconds.

Question 16

Two trains start from the same station at the same time, moving in opposite directions. Train P travels at 72 km/h and Train Q travels at 48 km/h. After how many hours will they be 360 km apart?

Accepted Answer

Step 1: When two trains move in opposite directions from the same point, their relative speed = Sum of their speeds = 72 + 48 = 120 km/h. Step 2: Time to be 360 km apart = Distance ÷ Relative Speed = 360 ÷ 120 = 3 hours.

Question 17

A train 200 m long passes a stationary pole in 10 seconds. How long will it take to pass another train of length 300 m that is stationary on an adjacent track?

Accepted Answer

Step 1: Find the speed of the moving train using the pole crossing. When passing a pole, distance = train length = 200 m. Speed = 200 ÷ 10 = 20 m/s. Step 2: When passing another stationary train, total distance = length of first train + length of second train = 200 + 300 = 500 m. Step 3: Time = Distance ÷ Speed = 500 ÷ 20 = 25 seconds.

Question 18

A train 200 m long crosses a pole in 10 seconds. How long will it take to cross a bridge of length 300 m?

Accepted Answer

Step 1: When a train crosses a pole (point object), distance covered = length of train only. Distance = 200 m, Time = 10 seconds. Speed = 200 ÷ 10 = 20 m/s. Step 2: When crossing a bridge, distance covered = length of train + length of bridge = 200 + 300 = 500 m. Step 3: Time = Distance ÷ Speed = 500 ÷ 20 = 25 seconds.

Question 19

Train A crosses a platform of length 150 m in 20 seconds. If the train's length is 250 m, what is the speed of Train A?

Accepted Answer

Step 1: When a train crosses a platform, total distance = train length + platform length = 250 + 150 = 400 m. Step 2: Speed = Distance ÷ Time = 400 ÷ 20 = 20 m/s.

Question 20

Two trains are moving towards each other on parallel tracks. Train X has a speed of 60 km/h and Train Y has a speed of 40 km/h. What is their relative speed?

Accepted Answer

Step 1: When two trains move towards each other, their relative speed is the sum of their individual speeds. Step 2: Relative speed = 60 + 40 = 100 km/h.

Question 21

Two trains are moving towards each other on parallel tracks. Train P travels at 45 km/h and Train Q travels at 55 km/h. If they are initially 400 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = Sum of individual speeds. Relative speed = 45 + 55 = 100 km/h. Step 2: Time to meet = Distance ÷ Relative speed = 400 ÷ 100 = 4 hours.

Question 22

Train P and Train Q are running on parallel tracks. Train P (length 120 m) is running at 72 km/h, and Train Q (length 80 m) is running at 54 km/h in the same direction. How much time will Train P take to completely overtake Train Q?

Accepted Answer

Step 1: Convert speeds to m/s: Train P = 72 × (5/18) = 20 m/s, Train Q = 54 × (5/18) = 15 m/s. Step 2: Relative speed = 20 - 15 = 5 m/s (same direction). Step 3: To completely overtake, Train P must cover the sum of both lengths = 120 + 80 = 200 m. Step 4: Time = Distance / Relative speed = 200 / 5 = 40 seconds.

Question 23

A train crosses a bridge of length 500 m in 60 seconds while running at a constant speed. The same train crosses a tunnel of length 300 m in 40 seconds. What is the length of the train?

Accepted Answer

Step 1: Let train length = L meters. Step 2: For bridge: (L + 500) ÷ 60 = Speed. Step 3: For tunnel: (L + 300) ÷ 40 = Speed. Step 4: Since speed is constant: (L + 500) ÷ 60 = (L + 300) ÷ 40. Step 5: 40(L + 500) = 60(L + 300). Step 6: 40L + 20000 = 60L + 18000. Step 7: 2000 = 20L. Step 8: L = 100 m.

Question 24

Two trains start simultaneously from stations X and Y, which are 360 km apart. Train P travels from X to Y at 60 km/h, and Train Q travels from Y to X at 90 km/h. At what distance from station X will they meet?

Accepted Answer

Step 1: Combined speed = 60 + 90 = 150 km/h. Step 2: Time to meet = 360 ÷ 150 = 2.4 hours. Step 3: Distance from X = Speed of Train P × Time = 60 × 2.4 = 144 km.

Question 25

Two trains start simultaneously from stations P and Q, which are 360 km apart. Train X travels from P to Q at 60 km/h, and Train Y travels from Q to P at 90 km/h. At what distance from station P will the two trains meet?

Accepted Answer

Step 1: Trains are moving towards each other, so relative speed = 60 + 90 = 150 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 360 ÷ 150 = 2.4 hours. Step 3: Distance covered by Train X from P = Speed of X × Time = 60 × 2.4 = 144 km.

Question 26

Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A to B at 60 km/h, and Train Y travels from B to A at 40 km/h. At what distance from station A will the two trains meet?

Accepted Answer

Step 1: When two objects move towards each other, relative speed = 60 + 40 = 100 km/h. Step 2: Time to meet = Total distance / Relative speed = 360 / 100 = 3.6 hours. Step 3: Distance covered by Train X from A = Speed × Time = 60 × 3.6 = 216 km.

Question 27

A train travels 360 km in 6 hours. If the train increases its speed by 25%, how much time will it take to cover the same distance?

Accepted Answer

Step 1: Original speed = 360 ÷ 6 = 60 km/h. Step 2: New speed = 60 + (25% of 60) = 60 + 15 = 75 km/h. Step 3: Time taken at new speed = 360 ÷ 75 = 4.8 hours = 4 hours 48 minutes.

Question 28

Two trains start simultaneously from stations A and B, which are 480 km apart. Train X travels from A to B at 60 km/h, and Train Y travels from B to A at 40 km/h. At what distance from station A will the two trains meet?

Accepted Answer

Step 1: Trains are moving towards each other, so relative speed = 60 + 40 = 100 km/h. Step 2: Time taken to meet = Total distance ÷ Relative speed = 480 ÷ 100 = 4.8 hours. Step 3: Distance covered by Train X from A = Speed × Time = 60 × 4.8 = 288 km.

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