A is standing on the foremost point of a train moving at 270 km/hr in ...
The speed of the train = 270 km/hr = 75 m/s The time after which the difference in position of A is 1800 m = 1800/(75 - 3) = 25 seconds Now, in these 25 seconds,
- A walks 25 x 3 = 75 m towards rearmost part of the train.
- B walks 25 x 4 = 100 m towards foremost point of the train.
At his stage, there is distance of 2100 m between them.
∴ The length of the train = 75 + 2100+100 = 2275 m
Hence, option 4.
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A is standing on the foremost point of a train moving at 270 km/hr in ...
Let's break down the problem step by step to find the length of the train.
1. Calculate the relative speed:
The relative speed between A and B is the sum of their individual speeds. Since A is moving in the opposite direction of the train at 3 m/s and the train is moving at 270 km/hr (which is 75 m/s), the relative speed between A and B is 3 + 75 = 78 m/s.
2. Calculate the time taken by A to cover 1800 m:
To find the time taken by A to cover 1800 m, we can use the formula distance = speed × time. Rearranging the formula, we have time = distance / speed. Substituting the given values, we get time taken by A = 1800 / 3 = 600 seconds.
3. Calculate the distance covered by B in the same time:
Since A and B are moving in opposite directions, the distance covered by B can be calculated by subtracting the distance covered by A from the total distance between them. Given that B is 2100 m away from A, the distance covered by B is 2100 + 1800 = 3900 m.
4. Calculate the time taken by B to cover 3900 m:
Using the formula distance = speed × time, we can rearrange the formula to find time = distance / speed. Substituting the given values, we get time taken by B = 3900 / 4 = 975 seconds.
5. Calculate the length of the train:
Now, we know that the time taken by A is 600 seconds and the time taken by B is 975 seconds. Since the train is moving at a constant speed, the ratio of the time taken by A to the time taken by B is equal to the ratio of their distances from the starting point of the train. Let's denote the length of the train as 'L'. Then, we have the equation:
600 / L = 975 / (L + 2100)
Cross-multiplying and simplifying the equation, we get:
600(L + 2100) = 975L
600L + 1260000 = 975L
375L = 1260000
L = 1260000 / 375
L = 3360 meters
Therefore, the length of the train is 3360 meters, which is not among the given options. However, the closest option is 2275 meters (option D).