(26) A train of length 390 meters is running at a speed of 72 km/hr. How long does it take to cross a 210-meter-long platform?
Answer : 30 seconds
Explanation
When a train crosses a platform, it covers the distance equal to its own length and the length of the platform.
Total distance covered by the train = Length of the train + Length of the platform Total distance = 390 meters + 210 meters = 600 meters
We need to convert the speed from km/hr to m/s, as the length of the train and platform is in meters.
Speed of the train = 72 km/hr Speed = (72 x 1000) / 3600 m/s = 20 m/s
Now we can use the formula:
Time = Distance / Speed
Time = 600 meters / 20 m/s = 30 seconds
Therefore, it will take 30 seconds for the train to cross the 210-meter-long platform.
(27) Two trains of lengths 480 meters and 580 meters are running on parallel lines in the opposite direction at 75 km/hr and 85 km/hr. In how many seconds will the trains pass each other?
Answer : 23.85 seconds
Explanation
When two trains of different lengths are running in opposite directions, the total distance they cover while passing each other is the sum of their lengths.
Total distance = Length of first train + Length of second train Total distance = 480 meters + 580 meters = 1060 meters
We need to convert the speeds from km/hr to m/s, as the lengths of the trains are in meters.
Speed of the first train = 75 km/hr Speed of the second train = 85 km/hr
Speed of first train = (75 x 1000) / 3600 m/s = 20.83 m/s Speed of second train = (85 x 1000) / 3600 m/s = 23.61 m/s
Now we can use the formula:
Time = Distance / Relative speed
Relative speed = Speed of first train + Speed of second train Relative speed = 20.83 m/s + 23.61 m/s = 44.44 m/s
Time = 1060 meters / 44.44 m/s ≈ 23.85 seconds
Therefore, it will take approximately 23.85 seconds for the trains to pass each other.
(28) Two trains of equal length are running on parallel lines in the opposite direction at 70 km/hr and 80 km/hr. The trains pass each other in 35 seconds. The length of each train is?
Answer : 727 meters.
Explanation
When two trains of equal length are running in opposite directions, the total distance they cover while passing each other is twice the length of each train.
Let’s assume the length of each train to be “x” meters.
Total distance = 2x meters
We need to convert the speeds from km/hr to m/s, as the lengths of the trains are in meters.
Speed of the first train = 70 km/hr Speed of the second train = 80 km/hr
Speed of first train = (70 x 1000) / 3600 m/s = 19.44 m/s Speed of second train = (80 x 1000) / 3600 m/s = 22.22 m/s
Now we can use the formula:
Time = Distance / Relative speed
Relative speed = Speed of first train + Speed of second train Relative speed = 19.44 m/s + 22.22 m/s = 41.66 m/s
Time = (2x) meters / 41.66 m/s = 35 seconds
Solving for “x”, we get:
x = (41.66 m/s x 35 s) / 2 = 727.1 meters
Therefore, the length of each train is approximately 727 meters.
(29) A train of length 540 meters is running at a speed of 96 km/hr. How long does it take to cross a 240-meter-long station?
Answer : 29.25 seconds
Explanation
When a train crosses a station, it covers the distance equal to its own length and the length of the station.
Total distance covered by the train = Length of the train + Length of the station Total distance = 540 meters + 240 meters = 780 meters
We need to convert the speed from km/hr to m/s, as the length of the train and station is in meters.
Speed of the train = 96 km/hr Speed = (96 x 1000) / 3600 m/s = 26.67 m/s
Now we can use the formula:
Time = Distance / Speed
Time = 780 meters / 26.67 m/s = 29.25 seconds
Therefore, it will take 29.25 seconds for the train to cross the 240-meter-long station.
(30) Two trains are running on parallel lines in the same direction at 25 km/hr and 45 km/hr. The faster train takes 150 seconds to pass the slower train. What is the length of the faster train?
Answer : 417 meters
Explanation
Let’s first convert the speeds from km/hr to m/s to make the units consistent with the time given in seconds:
Speed of the slower train = 25 km/hr = (251000)/(6060) m/s = 6.94 m/s
Speed of the faster train = 45 km/hr = (451000)/(6060) m/s = 12.5 m/s
Now, let’s consider the relative speed between the two trains, which is the difference between their speeds:
Relative speed = 12.5 – 6.94 = 5.56 m/s
We know that the faster train takes 150 seconds to pass the slower train, which means that the length of the combined trains is equal to the distance covered by the faster train in that time:
Distance covered by the faster train in 150 seconds = 150 * 12.5 = 1875 meters
Let’s denote the length of the slower train by L1 and the length of the faster train by L2. When the faster train passes the slower train, it needs to cover the length of both trains, which is L1 + L2. We can write an equation based on the time and relative speed:
L1 + L2 = (relative speed) * (time taken)
L1 + L2 = 5.56 * 150
L1 + L2 = 834 meters
We know that the length of the slower train is usually smaller than the length of the faster train, so we can make an assumption that L2 is equal to the total length of the trains (L1 + L2) minus the length of the slower train (L1):
L2 = (L1 + L2) – L1
L2 = 834 – L1
Substituting this into the previous equation, we get:
L1 + (834 – L1) = 834
L1 = 417 meters
Finally, we can calculate the length of the faster train by subtracting the length of the slower train from the total length of the combined trains:
L2 = 834 – 417 = 417 meters
Therefore, the length of the faster train is 417 meters.
