A train traveling at 48 kmph completely crosses another train having half its length and travelling in the opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

To solve this problem, we need to find the length of the first train and then use that information to find the length of the platform.

Step 1: Find the relative speed of the two trains. Since they are moving in opposite directions, we add their speeds. Convert the km/hr to m/s by multiplying by 5/18. So, the relative speed is (48+42) * 5/18 = 50 m/s.

Step 2: The time it takes for the trains to cross each other is 12 seconds. The formula to find the distance when speed and time are known is Distance = Speed * Time. So, the total length of the two trains is 50 m/s * 12 s = 600 m.

Step 3: The length of the second train is half that of the first train. Let's denote the length of the first train as L. So, the length of the second train is L/2. The total length of the two trains is L + L/2 = 600 m. Solving this equation gives L = 400 m. So, the length of the first train is 400 m.

Step 4: The time it takes for the first train to cross the platform is 45 seconds. The speed of the first train is 48 km/hr, which is 48 * 5/18 = 13.33 m/s.

Step 5: The distance the train travels to cross the platform is the length of the train plus the length of the platform. Let's denote the length of the platform as P. So, the total distance is L + P = 13.33 m/s * 45 s.

Step 6: Solving the equation L + P = 13.33 m/s * 45 s for P gives P = 13.33 m/s * 45 s - L = 600 m - 400 m = 200 m.

So, the length of the platform is 200 m.