The correct option is A 67 kg.
Let Arun's weight by X kg.
According to Arun, 65 < X < 72
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
∴ Required average = (66+67+683)=(2013) = 67 kg.