Since the train crosses the man, distance covered by the train is equal to the length of the train =L(say)
Speed = 54 km/hr = 54 x 5/18 m/s =15 m/sec and time taken = 20 sec
Length of the train is L= 20 x 15 = 300 m
While crossing platform,the distance covered by the train is equal to the length of train + length of the platform = L+P
Time taken =36 sec
L+P = 36 x15
300 + P = 540
P = 240 m