Question 1

Two trains start simultaneously from opposite ends of a 600 km track. Train X travels at 80 km/h and Train Y at 70 km/h. A bird starts flying from the front of Train X towards Train Y at 120 km/h. When the bird meets Train Y, it immediately turns back and flies towards Train X. This process continues until the trains meet. What is the total distance covered by the bird?

Accepted Answer

Step 1: The key insight is that the bird keeps flying until the two trains meet, regardless of how many times it changes direction. Step 2: Time taken for the trains to meet = Total distance ÷ Relative speed = 600 ÷ (80 + 70) = 600 ÷ 150 = 4 hours. Step 3: The bird flies continuously for these 4 hours at 120 km/h. Step 4: Total distance covered by the bird = Speed of bird × Time = 120 × 4 = 480 km. Therefore, the bird covers 480 km in total.

Question 2

A train starts from station A and travels towards station B at 72 km/h. After 3 hours, another train starts from station B towards station A at 90 km/h. If the distance between A and B is 540 km, at what distance from station A will the two trains meet?

Accepted Answer

Step 1: In 3 hours, the first train covers: 72 × 3 = 216 km from A. Step 2: Remaining distance between the two trains = 540 - 216 = 324 km. Step 3: Now both trains move towards each other with relative speed = 72 + 90 = 162 km/h. Step 4: Time to meet after the second train starts = 324 ÷ 162 = 2 hours. Step 5: Distance covered by the first train in these 2 hours = 72 × 2 = 144 km. Step 6: Total distance from A = 216 + 144 = 360 km. Therefore, the trains meet at 360 km from station A.

Question 3

Two trains of lengths 120 m and 180 m are moving in the same direction on parallel tracks. The faster train (120 m) travels at 90 km/h and the slower train (180 m) at 54 km/h. How long will it take for the faster train to completely overtake the slower train?

Accepted Answer

Step 1: Convert speeds to m/s: 90 km/h = 90 × (5/18) = 25 m/s; 54 km/h = 54 × (5/18) = 15 m/s. Step 2: Relative speed = 25 - 15 = 10 m/s (same direction). Step 3: Total distance to cover for complete overtaking = Length of both trains = 120 + 180 = 300 m. Step 4: Time = Distance ÷ Relative speed = 300 ÷ 10 = 30 seconds. Therefore, the faster train takes 30 seconds to completely overtake the slower train.

Question 4

A train crosses a platform of length 150 m in 18 seconds and crosses a pole in 12 seconds. What is the length of the train?

Accepted Answer

Step 1: Let the length of the train be L metres. When crossing a pole, the train travels its own length: L = Speed × 12. Step 2: When crossing the platform, the train travels L + 150: L + 150 = Speed × 18. Step 3: From equation 1, Speed = L/12. Substituting in equation 2: L + 150 = (L/12) × 18 = 1.5L. Step 4: 150 = 1.5L - L = 0.5L, so L = 300 m. Therefore, the length of the train is 300 m.

Question 5

Two trains are moving towards each other. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are 200 km apart, how long will it take for them to meet?

Accepted Answer

Step 1: When trains move towards each other, relative speed = Speed of A + Speed of B = 60 + 40 = 100 km/h. Step 2: Time = Distance ÷ Relative Speed = 200 ÷ 100 = 2 hours. Therefore, they will meet in 2 hours.

Question 6

A train 150 metres long passes a stationary pole in 5 seconds. What is the speed of the train in m/s?

Accepted Answer

Step 1: When a train passes a pole, the distance covered equals the length of the train = 150 metres. Step 2: Speed = Distance ÷ Time = 150 ÷ 5 = 30 m/s. Therefore, the speed is 30 m/s.

Question 7

A train 200 metres long passes another train 150 metres long moving in the same direction. Train A travels at 80 km/h and Train B travels at 50 km/h. How long will it take for Train A to completely pass Train B?

Accepted Answer

Step 1: When trains move in the same direction, relative speed = Speed of A − Speed of B = 80 − 50 = 30 km/h. Step 2: Convert to m/s: 30 × (5/18) = 8.33 m/s. Step 3: Distance to cover = Length of A + Length of B = 200 + 150 = 350 metres. Step 4: Time = 350 ÷ 8.33 ≈ 42 seconds. Therefore, it takes approximately 42 seconds.

Question 8

A train travels 360 km in 6 hours. If it increases its speed by 20 km/h, how long will it take to cover the same distance?

Accepted Answer

Step 1: Original speed = 360 ÷ 6 = 60 km/h. Step 2: New speed = 60 + 20 = 80 km/h. Step 3: Time at new speed = 360 ÷ 80 = 4.5 hours. Therefore, it will take 4.5 hours.

Question 9

A train travels 240 km in 4 hours at a constant speed. What is the speed of the train in km/h?

Accepted Answer

Step 1: Use the formula Speed = Distance ÷ Time. Step 2: Speed = 240 ÷ 4 = 60 km/h. Therefore, the speed of the train is 60 km/h.

Question 10

A train covers 180 metres in 9 seconds. How long will it take to cover 400 metres at the same speed?

Accepted Answer

Step 1: Find speed using Speed = Distance ÷ Time = 180 ÷ 9 = 20 m/s. Step 2: Use Time = Distance ÷ Speed = 400 ÷ 20 = 20 seconds. Therefore, the train takes 20 seconds.

Question 11

Train A of length 150 m crosses a stationary platform in 15 seconds. Train B of length 100 m travels at twice the speed of Train A. How long will Train B take to cross the same platform?

Accepted Answer

Step 1: Find speed of Train A. Distance = Length of train + Platform length. For a platform crossing, we assume platform length is negligible or the train fully crosses in the given time. Speed of A = 150 m ÷ 15 s = 10 m/s. Step 2: Speed of Train B = 2 × 10 = 20 m/s. Step 3: Time for Train B to cross platform = 100 m ÷ 20 m/s = 5 seconds.

Question 12

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: Original speed = 240 km ÷ 4 hours = 60 km/h. Step 2: New speed = 60 + (20% of 60) = 60 + 12 = 72 km/h. Step 3: Distance at new speed in 5 hours = 72 × 5 = 360 km.

Question 13

Train P (length 120 m) and Train Q (length 80 m) are moving in the same direction on parallel tracks. Train P travels at 90 km/h and Train Q at 54 km/h. How many seconds will it take for Train P to completely overtake Train Q?

Accepted Answer

Step 1: When trains move in the same direction, relative speed = Difference of speeds = 90 − 54 = 36 km/h. Step 2: Convert to m/s: 36 km/h = 36 × (5/18) = 10 m/s. Step 3: To completely overtake, Train P must cover a distance equal to the sum of both lengths = 120 + 80 = 200 m. Step 4: Time = 200 m ÷ 10 m/s = 20 seconds.

Question 14

Two trains start simultaneously from stations P and Q, which are 360 km apart. Train X travels from P towards Q at 60 km/h, and Train Y travels from Q towards P at 40 km/h. After how many hours will they meet?

Accepted Answer

Step 1: When two trains travel towards each other, their relative speed = Sum of individual speeds = 60 + 40 = 100 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 360 km ÷ 100 km/h = 3.6 hours.

Question 15

A train 200 m long is running at 72 km/h. How long will it take to pass a man standing on the platform?

Accepted Answer

Step 1: Convert speed from km/h to m/s: 72 km/h = 72 × (5/18) m/s = 20 m/s. Step 2: To pass a stationary man, the train must cover a distance equal to its own length = 200 m. Step 3: Time = Distance ÷ Speed = 200 m ÷ 20 m/s = 10 seconds.

Question 16

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 they meet, and at what distance from station P?

Accepted Answer

Step 1: When two trains move 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 P = Speed of Train A × Time = 60 × 4.8 = 288 km. Therefore, they meet after 4.8 hours at 288 km from station P.

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