1
A train 120 meters long takes 30 seconds to cross a pole. What is the speed of the train in km/h?
Solution:
Step 1: When a train crosses a pole, it covers its own length.
Step 2: Distance = 120 meters, Time = 30 seconds.
Step 3: Speed = Distance / Time = 120 / 30 = 4 m/s.
Step 4: To convert m/s to km/h, multiply by 18/5: 4 × 18/5 = 14.4 km/h.
Final Answer: 14.4 km/h
2
A 150 m long train passes a platform 100 m long in 25 seconds. What is the speed of the train in m/s?
Solution:
Step 1: Total distance covered = Length of train + Length of platform = 150 + 100 = 250 m.
Step 2: Time = 25 seconds.
Step 3: Speed = Distance / Time = 250 / 25 = 10 m/s.
Final Answer: 10 m/s
3
A train 180 m long is running at 54 km/h. How much time will it take to cross a man standing on the platform?
Solution:
Step 1: Convert speed to m/s: 54 × 5/18 = 15 m/s.
Step 2: Time = Distance / Speed = 180 / 15 = 12 seconds.
Final Answer: 12 seconds
4
A train 200 m long passes a bridge 300 m long in 40 seconds. Find the speed of the train in km/h.
Solution:
Step 1: Total distance = 200 + 300 = 500 m.
Step 2: Time = 40 seconds.
Step 3: Speed = 500 / 40 = 12.5 m/s.
Step 4: Convert to km/h: 12.5 × 18/5 = 45 km/h.
Final Answer: 45 km/h
5
A train running at 36 km/h crosses a platform 90 m long in 30 seconds. Find the length of the train.
Solution:
Step 1: Convert speed to m/s: 36 × 5/18 = 10 m/s.
Step 2: Distance covered in 30 seconds = 10 × 30 = 300 m.
Step 3: Length of train = Total distance - Length of platform = 300 - 90 = 210 m.
Final Answer: 210 m
6
A train 250 m long passes a man walking at 5 km/h in the same direction as the train. The train is moving at 45 km/h. How long will it take to pass the man?
Solution:
Step 1: Relative speed = 45 - 5 = 40 km/h.
Step 2: Convert to m/s: 40 × 5/18 = 11.11 m/s.
Step 3: Time = 250 / 11.11 ≈ 22.5 seconds.
Final Answer: 22.5 seconds
7
A train 300 m long is running at 72 km/h. In how many seconds will it cross a platform 200 m long?
Solution:
Step 1: Convert speed to m/s: 72 × 5/18 = 20 m/s.
Step 2: Total distance = 300 + 200 = 500 m.
Step 3: Time = 500 / 20 = 25 seconds.
Final Answer: 25 seconds
8
A train 100 m long passes a man running at 10 km/h in the opposite direction. The train is moving at 54 km/h. How long will it take to pass the man?
Solution:
Step 1: Relative speed = 54 + 10 = 64 km/h.
Step 2: Convert to m/s: 64 × 5/18 ≈ 17.78 m/s.
Step 3: Time = 100 / 17.78 ≈ 5.6 seconds.
Final Answer: 5.6 seconds
9
Two trains, each 120 m long, are running in opposite directions at 60 km/h and 40 km/h. How long will they take to cross each other?
Solution:
Step 1: Relative speed = 60 + 40 = 100 km/h.
Step 2: Convert to m/s: 100 × 5/18 ≈ 27.78 m/s.
Step 3: Total distance = 120 + 120 = 240 m.
Step 4: Time = 240 / 27.78 ≈ 8.64 seconds.
Final Answer: 8.64 seconds
10
A train 90 m long passes a platform 60 m long in 9 seconds. Find the speed of the train in km/h.
Solution:
Step 1: Total distance = 90 + 60 = 150 m.
Step 2: Time = 9 seconds.
Step 3: Speed = 150 / 9 ≈ 16.67 m/s.
Step 4: Convert to km/h: 16.67 × 18/5 = 60 km/h.
Final Answer: 60 km/h
11
A train 400 m long passes a man standing on a platform in 20 seconds. Find the speed of the train in km/h.
Solution:
Step 1: Speed = 400 / 20 = 20 m/s.
Step 2: Convert to km/h: 20 × 18/5 = 72 km/h.
Final Answer: 72 km/h
12
A train 150 m long passes another train 100 m long running in the same direction at 36 km/h in 18 seconds. The speed of the first train is 54 km/h. Find the time taken to cross each other completely.
Solution:
Step 1: Relative speed = 54 - 36 = 18 km/h.
Step 2: Convert to m/s: 18 × 5/18 = 5 m/s.
Step 3: Total distance = 150 + 100 = 250 m.
Step 4: Time = 250 / 5 = 50 seconds.
Final Answer: 50 seconds
13
A train 180 m long passes a platform 120 m long in 15 seconds. Find the speed of the train in m/s and km/h.
Solution:
Step 1: Total distance = 180 + 120 = 300 m.
Step 2: Time = 15 seconds.
Step 3: Speed = 300 / 15 = 20 m/s.
Step 4: Convert to km/h: 20 × 18/5 = 72 km/h.
Final Answer: 20 m/s or 72 km/h
14
A train 120 m long passes a man running at 6 km/h in the same direction in 12 seconds. The speed of the train is 54 km/h. Find the time taken to pass the man.
Solution:
Step 1: Relative speed = 54 - 6 = 48 km/h.
Step 2: Convert to m/s: 48 × 5/18 = 13.33 m/s.
Step 3: Time = 120 / 13.33 ≈ 9 seconds.
Final Answer: 9 seconds
15
A train 200 m long passes a tunnel 300 m long in 25 seconds. Find the speed of the train in m/s and km/h.
Solution:
Step 1: Total distance = 200 + 300 = 500 m.
Step 2: Time = 25 seconds.
Step 3: Speed = 500 / 25 = 20 m/s.
Step 4: Convert to km/h: 20 × 18/5 = 72 km/h.
Final Answer: 20 m/s or 72 km/h
16
Two trains, 150 m and 100 m long, are running in the same direction at 50 km/h and 30 km/h. How long will it take for the faster train to pass the slower one?
Solution:
Step 1: Relative speed = 50 - 30 = 20 km/h.
Step 2: Convert to m/s: 20 × 5/18 ≈ 5.56 m/s.
Step 3: Total distance = 150 + 100 = 250 m.
Step 4: Time = 250 / 5.56 ≈ 45 seconds.
Final Answer: 45 seconds
17
A train 180 m long passes a platform 120 m long in 12 seconds. Find the speed of the train in m/s and km/h.
Solution:
Step 1: Total distance = 180 + 120 = 300 m.
Step 2: Time = 12 seconds.
Step 3: Speed = 300 / 12 = 25 m/s.
Step 4: Convert to km/h: 25 × 18/5 = 90 km/h.
Final Answer: 25 m/s or 90 km/h
18
A train 120 m long passes a man running at 12 km/h in the opposite direction in 6 seconds. The speed of the train is 60 km/h. Find the time taken to pass the man.
Solution:
Step 1: Relative speed = 60 + 12 = 72 km/h.
Step 2: Convert to m/s: 72 × 5/18 = 20 m/s.
Step 3: Time = 120 / 20 = 6 seconds.
Final Answer: 6 seconds
19
A train 250 m long passes a platform 150 m long in 20 seconds. Find the speed of the train in m/s and km/h.
Solution:
Step 1: Total distance = 250 + 150 = 400 m.
Step 2: Time = 20 seconds.
Step 3: Speed = 400 / 20 = 20 m/s.
Step 4: Convert to km/h: 20 × 18/5 = 72 km/h.
Final Answer: 20 m/s or 72 km/h
20
Two trains, each 100 m long, are running in opposite directions at 30 km/h and 45 km/h. How long will they take to cross each other?
Solution:
Step 1: Relative speed = 30 + 45 = 75 km/h.
Step 2: Convert to m/s: 75 × 5/18 ≈ 20.83 m/s.
Step 3: Total distance = 100 + 100 = 200 m.
Step 4: Time = 200 / 20.83 ≈ 9.6 seconds.
Final Answer: 9.6 seconds