---

Solution

Speed of train $= 108 imes frac{5}{18} = 30$ m/s
Speed of man $= 12 imes frac{5}{18} = frac{10}{3}$ m/s
Relative speed $= 30 - frac{10}{3} = frac{80}{3}$ m/s
Length of train $= frac{80}{3} imes 9 = 240$ m
Train length + platform length $= 30 imes 30 = 900$ m
Platform length $= 900 - 240 = 660$ m
Hence, the answer is 240 and 660.

---

Solution

Distances are proportional to speeds.
Ratio $= 50:55 = 10:11$
Difference $= 1$ part $= 20$ km
Total distance $= 21 imes 20 = 420$ km
Hence, the distance is 420 km.