The correct answer is option (B):
150m
Here's how to solve this problem, breaking it down step-by-step to understand why 150m is the correct answer:
The key concept here is that when a train crosses a platform or a bridge, it covers its own length plus the length of the platform or bridge. The speed of the train remains constant in both scenarios.
Let's use the following:
* 'L' = Length of the train (in meters)
* 'S' = Speed of the train (in meters per second)
Scenario 1: Crossing the platform (1200m)
* Distance covered = L + 1200 m
* Time taken = 15 seconds
* Therefore: S = (L + 1200) / 15 ...(Equation 1)
Scenario 2: Crossing the bridge (3 km = 3000 m)
* Distance covered = L + 3000 m
* Time taken = 35 seconds
* Therefore: S = (L + 3000) / 35 ...(Equation 2)
Since the speed (S) is the same in both scenarios, we can equate Equation 1 and Equation 2:
(L + 1200) / 15 = (L + 3000) / 35
Now we solve for L (the length of the train):
1. Cross-multiply: 35 * (L + 1200) = 15 * (L + 3000)
2. Expand: 35L + 42000 = 15L + 45000
3. Subtract 15L from both sides: 20L + 42000 = 45000
4. Subtract 42000 from both sides: 20L = 3000
5. Divide both sides by 20: L = 150
Therefore, the length of the train is 150 meters.