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?	Pick one:
A) 435 hectares.
B) 425 hectares.
C) 445 hectares.
D) 415 hectares.
E) 405 hectares.
Let the areas of the parts be x hectares and (900 - x) hectares.   Difference of the areas of the two parts = x - (900 - x) = 2x - 900   one-fifth of the average of the two areas = 1/5[x+(900−x)]/2   = 1/5 × (900/2)= 
<gadget id="calculator">(900/2)</gadget>
<output>450</output>
450/5= 
<gadget id="calculator">450/5</gadget>
<output>90</output>
90   Given that difference of the areas of the two parts= one-fifth of the average of the two areas   =&gt; 2x - 900 = 90   =&gt; 2x = 990   ⇒ x = 990/2= 
<gadget id="calculator">990/2</gadget>
<output>495</output>
495   Hence, area of smaller part= (900 - x) = (900 – 495) = 405 hectares.   Answer is 405 hectares..
<result>E</result>
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?