A large field of 900 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares? Choose the correct option:
A) 435 hectares .	B) 425 hectares .	C) 445 hectares .	D) 415 hectares .	E) 405 hectares .

Rationale: "let the areas of the parts be x hectares and ( 900 - x ) hectares . difference of the areas of the two parts = x - ( 900 - x ) = 2 x - 900 one - fifth of the average of the two areas = 1 / 5 [ x + ( 900 − x ) ] / 2 = 1 / 5 × ( 900 / 2 ) = 450 / 5 = 90 given that difference of the areas of the two parts = one - fifth of the average of the two areas = > 2 x - 900 = 90 = > 2 x = 990 ⇒ x = 990 / 2 = 495 hence , area of smaller part = ( 900 - x ) = ( 900 – 495 ) = 405 hectares . answer is e ."
Answer: E