A train running at 24 km/h takes 12 seconds to pass a platform. Next, it takes 8 seconds to pass a man walking at 8 km/h in the same direction. Find the length of the platform and the length of the train.

Let the length of the train be L m. 

Let the length of the platform be l m.

Speed of the train (V) = 24 km/h = 24 * 5/18 = 20/3 m/s

Speed of the man (v) = 8 km/h = 8 * 5/18 = 20/9 m/s

The train takes 8 seconds to pass the man. 

So, t = L/(V - v) 

8 = L/(20/3 - 20/9) 

L = 320/9

L = 35.55 m = 36 m (approximately) 

So, length of the train = 36 m 

Now, the train takes 12 seconds to cross the platform. 

So, t = (L + l)/V 

12 = (320/9 + l)/(20/3) 

l = 400/9

l = 44.44 m = 44 m (approximately) 

So, the length of the platform is 45 m and that of the train is 36 m.