A 300 m long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?A. 250 mB. 300 mC. 350 mD. 120 m

Let's denote the length of the train as "T" meters and the length of the platform as "P" meters.

We are given that the train crosses a platform in 39 seconds, so the time it takes to cross both the train and the platform is 39 seconds. We are also given that the train crosses a signal pole in 18 seconds.

When the train crosses a signal pole, it only covers its own length, which is T meters. So, the speed of the train is:

Speed of train = Distance / Time
Speed of train = T / 18 (in meters per second)

When the train crosses both the train and the platform, it covers a total distance of T (train length) + P (platform length), which is 300 meters (the length of the train). The time taken for this is 39 seconds. So, the speed of the train is:

Speed of train = Distance / Time
Speed of train = (T + P) / 39 (in meters per second)

Since the speed of the train is the same in both cases, we can set the two expressions for the speed of the train equal to each other:

T / 18 = (T + P) / 39

Now, we can solve for P (the length of the platform):

T / 18 = (T + P) / 39

Cross-multiply to get rid of the fractions:

39T = 18(T + P)

Now, expand and solve for P:

39T = 18T + 18P

Subtract 18T from both sides:

21T = 18P

Divide both sides by 18:

P = (21T) / 18

P = (7/6)T

Now, we know the length of the train is 300 meters (T = 300). Plug this value into the equation for P:

P = (7/6) * 300

P = 350 meters

So, the length of the platform is 350 meters.

Therefore, the correct answer is option C: 350 m.