A train overtakes two persons who are walking in the same direction in which the train is running, at the rates of 3 kmph and 5 kmph, and passes them completely in 10 and 12 seconds, respectively. Find the length of the train.

Let the speed of the train be x m/s.

Then, speed of the train in the same direction with respect to first person = x - 3 * 5/18 = (x - 5/6) m/s 

Now, speed of the train in the same direction with respect to second person = x - 5 * 5/18 = (x - 25/18) m/s 

So, length of the train is (x - 5/6) * 10 = (x - 25/18) * 25/18.

After solving, we get

x = 25/3 m/s

So, the speed of the train is 25/3 m/s,

Then, length of the train is (25/3 - 5/6) * 10 = 75 m.