Final answer:
Correct option: b. 140 m
To find the length of the platform, we determine the train's speed by dividing the train's length by the time it takes to pass a man, and then use that speed to calculate the total distance covered while passing the platform. Subtracting the train's length from this distance gives the length of the platform, which is 140 meters.
Step-by-step explanation:
To solve the problem, we first need to determine the speed of the train.
Since the train crosses a man (i.e., passes by a point) in 15 seconds, and the train's length is 105 meters, we can calculate the speed (speed of train) using the formula speed = distance / time.
Speed of train = 105 m / 15 s = 7 m/s
Next, we know that the train crosses a platform in 35 seconds.
To find the length of the platform (length of platform), we have to consider both the length of the train and the time it takes to cross the entire platform.
Since the speed of the train is constant, the distance covered by the train while crossing the platform is the combined length of the train and the platform.
Distance covered = Speed of train * Time to cross
= 7 m/s * 35 s
Distance covered = 245 meters
The distance covered is the sum of the lengths of the train and the platform.
To find the length of the platform alone, we subtract the length of the train from the total distance covered:
Length of platform = Distance covered - Length of train
Length of platform = 245 m - 105 m
= 140 meters
Therefore, the length of the platform is 140 meters, which corresponds to option b.