Question 1

A train 100 m long crosses another train 150 m long moving in the opposite direction in 10 seconds. If the first train travels at 54 km/h, what is the speed of the second train in km/h?

Accepted Answer

Step 1: When trains move in opposite directions, relative speed = Sum of speeds. Total distance = 100 + 150 = 250 m. Step 2: Relative speed = Distance ÷ Time = 250 ÷ 10 = 25 m/s. Step 3: Convert to km/h: 25 × (18/5) = 90 km/h. Step 4: Speed of second train = Relative speed - Speed of first train = 90 - 54 = 36 km/h.

Question 2

A train travels 288 km in 4 hours. What is the speed of the train in m/s?

Accepted Answer

Step 1: Calculate speed in km/h. Speed = 288 ÷ 4 = 72 km/h. Step 2: Convert to m/s by multiplying by 5/18. Speed = 72 × (5/18) = 360/18 = 20 m/s.

Question 3

A runner jogs at 12 km/h and a cyclist rides at 18 km/h, both starting from the same point in the same direction. After 2 hours, how far ahead is the cyclist from the runner?

Accepted Answer

Step 1: The relative speed between the cyclist and runner is 18 - 12 = 6 km/h (since they move in the same direction). Step 2: After 2 hours, the distance covered by the cyclist relative to the runner is: Distance = Relative Speed × Time = 6 × 2 = 12 km. Therefore, the cyclist is 12 km ahead.

Question 4

Two cars start from the same location and travel towards each other on a straight road. Car P travels at 55 km/h and Car Q travels at 65 km/h. If they meet after 4 hours, what was the initial distance between them?

Accepted Answer

Step 1: Since the cars travel towards each other, their relative speed is the sum of their individual speeds. Relative speed = 55 + 65 = 120 km/h. Step 2: Distance = Relative Speed × Time = 120 × 4 = 480 km. Therefore, the initial distance between them was 480 km.

Question 5

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are 300 km apart, how long will it take for them to meet?

Accepted Answer

Step 1: When two trains move towards each other, their relative speed is the sum of their individual speeds. Relative speed = 60 + 40 = 100 km/h. Step 2: Time = Distance ÷ Relative Speed = 300 ÷ 100 = 3 hours.

Question 6

A train 150 m long is moving at 72 km/h. How long will it take to cross a platform that is 350 m long?

Accepted Answer

Step 1: Convert speed from km/h to m/s: 72 km/h = 72 × (5/18) = 20 m/s. Step 2: Total distance to be covered = Length of train + Length of platform = 150 + 350 = 500 m. Step 3: Time = Distance ÷ Speed = 500 ÷ 20 = 25 seconds.

Question 7

A train passes a stationary pole in 8 seconds. If the train is 240 m long, what is its speed in km/h?

Accepted Answer

Step 1: When a train passes a pole, it covers a distance equal to its own length. Distance = 240 m, Time = 8 seconds. Step 2: Speed = Distance ÷ Time = 240 ÷ 8 = 30 m/s. Step 3: Convert to km/h: 30 × (18/5) = 30 × 3.6 = 108 km/h.

Question 8

Train A and Train B are moving in the same direction on parallel tracks. Train A travels at 72 km/h and Train B travels at 54 km/h. If Train A is 500 m behind Train B, how long will it take for Train A to catch up with Train B?

Accepted Answer

Step 1: When two trains move in the same direction, relative speed = Difference of speeds = 72 - 54 = 18 km/h. Step 2: Convert to m/s: 18 km/h = 18 × (5/18) = 5 m/s. Step 3: Time = Distance ÷ Relative Speed = 500 ÷ 5 = 100 seconds.

Question 9

Two trains of lengths 150 m and 100 m are running towards each other on parallel tracks at speeds of 50 km/h and 40 km/h respectively. How many seconds will they take to completely pass each other?

Accepted Answer

Step 1: Convert speeds to m/s: 50 km/h = 50 × (5/18) = 13.89 m/s (approx), 40 km/h = 40 × (5/18) = 11.11 m/s (approx). Step 2: For cleaner calculation: relative speed = 50 + 40 = 90 km/h = 90 × (5/18) = 25 m/s. Step 3: Total distance to cover = 150 + 100 = 250 m. Step 4: Time = 250 ÷ 25 = 10 seconds.

Question 10

Two trains start simultaneously from stations X and Y, which are 360 km apart. Train P travels from X towards Y at 60 km/h, and Train Q travels from Y towards X at 40 km/h. After 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 = 60 + 40 = 100 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 360 ÷ 100 = 3.6 hours.

Question 11

A train travels 240 km in 4 hours. If the train increases its speed by 20%, how much distance will it cover in 5 hours at the new speed?

Accepted Answer

Step 1: Find the original speed. Speed = Distance ÷ Time = 240 ÷ 4 = 60 km/h. Step 2: Calculate the new speed after 20% increase. New speed = 60 + (20% of 60) = 60 + 12 = 72 km/h. Step 3: Distance covered in 5 hours at new speed = 72 × 5 = 360 km.

Question 12

A train 200 m long takes 20 seconds to pass a man standing on the platform. The same train takes 50 seconds to completely cross a bridge. What is the length of the bridge?

Accepted Answer

Step 1: Find the speed of the train using the man-crossing data. When a train passes a man, it covers its own length. Speed = 200 m ÷ 20 s = 10 m/s. Step 2: When the train crosses the bridge, it must cover its own length plus the bridge length. Distance = Speed × Time = 10 × 50 = 500 m. Step 3: Length of bridge = Total distance − Train length = 500 − 200 = 300 m.

Question 13

Train X and Train Y are moving in the same direction on parallel tracks. Train X (length 120 m) travels at 80 km/h, and Train Y (length 80 m) travels at 60 km/h. How long will it take for Train X to completely overtake Train Y?

Accepted Answer

Step 1: Convert speeds to m/s. Train X: 80 km/h = 80 × (5/18) = 22.22 m/s ≈ 22.22 m/s. Train Y: 60 km/h = 60 × (5/18) = 16.67 m/s ≈ 16.67 m/s. Step 2: Relative speed = 22.22 − 16.67 = 5.56 m/s. Step 3: For complete overtaking, Train X must cover its own length plus Train Y's length = 120 + 80 = 200 m. Step 4: Time = 200 ÷ 5.56 = 36 seconds.

Question 14

Two trains start from the same station at the same time. Train M travels at 50 km/h and Train N travels at 70 km/h, both in the same direction. After 3 hours, Train N stops for 30 minutes. How much further ahead is Train N than Train M when Train N resumes its journey?

Accepted Answer

Step 1: Distance covered by Train M in 3 hours = 50 × 3 = 150 km. Step 2: Distance covered by Train N in 3 hours = 70 × 3 = 210 km. Step 3: When Train N stops for 30 minutes, Train M continues. In 0.5 hours, Train M covers = 50 × 0.5 = 25 km. Step 4: Distance of Train M after 3.5 hours = 150 + 25 = 175 km. Step 5: Distance of Train N when it resumes = 210 km. Step 6: Difference = 210 − 175 = 35 km.

Question 15

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

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Step 2: Relative speed = 60 + 40 = 100 km/h. Step 3: Time = Distance ÷ Relative speed = 500 ÷ 100 = 5 hours.

Question 16

A man cycles at 15 km/h and a woman cycles at 10 km/h in the same direction on the same road. If the woman starts 30 km ahead, how long will it take the man to catch up with the woman?

Accepted Answer

Step 1: When both move in the same direction, relative speed = faster speed − slower speed = 15 − 10 = 5 km/h. Step 2: The man needs to cover the initial gap of 30 km at the relative speed. Step 3: Time = Distance ÷ Relative speed = 30 ÷ 5 = 6 hours.

Question 17

Two cyclists start from the same point and travel in opposite directions. Cyclist A travels at 18 km/h and Cyclist B travels at 12 km/h. After how many hours will they be 90 km apart?

Accepted Answer

Step 1: When two objects move in opposite directions, their relative speed is the sum of their speeds. Step 2: Relative speed = 18 + 12 = 30 km/h. Step 3: Time = Distance ÷ Relative speed = 90 ÷ 30 = 3 hours.

Question 18

A train 240 metres long is travelling at 45 km/h. How long will it take to pass a stationary pole?

Accepted Answer

Step 1: Convert train speed to m/s: 45 km/h = 45 × (5/18) = 12.5 m/s. Step 2: To pass a pole, the train must cover a distance equal to its own length (240 m). Step 3: Time = Distance ÷ Speed = 240 ÷ 12.5 = 19.2 seconds.

Question 19

Two trains start from the same station at the same time. Train X travels at 80 km/h, and train Y travels at 60 km/h, both in the same direction. After 3 hours, train X stops for 30 minutes due to a breakdown. Train Y continues without stopping. How far apart will the two trains be 5 hours after they started?

Accepted Answer

Step 1: In the first 3 hours, train X travels = 80 × 3 = 240 km. In the first 3 hours, train Y travels = 60 × 3 = 180 km. Step 2: At 3 hours, train X is ahead by 240 - 180 = 60 km. Step 3: Train X stops for 30 minutes (0.5 hours). During this 0.5 hours, train Y travels = 60 × 0.5 = 30 km. Step 4: After the breakdown (at 3.5 hours), train X is at 240 km, train Y is at 180 + 30 = 210 km. Gap = 240 - 210 = 30 km. Step 5: From 3.5 hours to 5 hours, time elapsed = 5 - 3.5 = 1.5 hours. In 1.5 hours, train X travels = 80 × 1.5 = 120 km. In 1.5 hours, train Y travels = 60 × 1.5 = 90 km. Step 6: At 5 hours, train X is at 240 + 120 = 360 km. Train Y is at 210 + 90 = 300 km. Step 7: Distance apart = 360 - 300 = 60 km. Therefore, the trains are 60 km apart.

Question 20

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, while Train Y travels from B to A at 40 km/h. A bird flies back and forth between the two trains at a constant speed of 80 km/h, starting from Train X. What is the total distance covered by the bird from the moment the trains start until they meet?

Accepted Answer

Step 1: Find the time taken for the two trains to meet. Relative speed = 60 + 40 = 100 km/h (opposite directions). Time to meet = 480 ÷ 100 = 4.8 hours. Step 2: The bird flies continuously at 80 km/h for the entire 4.8 hours until the trains meet. Distance covered by bird = 80 × 4.8 = 384 km. Therefore, the answer is 384 km.

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