Let L be the length of the train, and let P be the length of the pole. We're given that the train takes 10 seconds to cross the pole and 20 seconds to cross a platform of length 200 meters.

When the train crosses the pole, it covers its own length, so we can write:

L = 10 * Train's Speed

When the train crosses the platform, it covers its own length plus the length of the platform, which is 200 meters, so we can write:

L + 200 = 20 * Train's Speed

Now, we can solve this system of equations. First, isolate Train's Speed in the first equation:

Train's Speed = L / 10

Now, substitute this expression for Train's Speed into the second equation:

L + 200 = 20 * (L / 10)

Simplify:

L + 200 = 2L

Now, subtract L from both sides:

200 = L

So, the length of the train (L) is 200 meters. Therefore, the length of the train is 200 meters.