A large field of 700 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?
400
365
385
315
Explanation:
Let the areas of the parts be x hectares and (700 - x) hectares
Difference of the areas of the two parts = x - (700 - x) = 2x - 700
one-fifth of the average of the two areas = $\dfrac{1}{5}\dfrac{[\text{x}+(700-\text{x})]}{2}$
$=\dfrac{1}{5} \times \dfrac{700}{2}=\dfrac{350}{5}=70$
Given that difference of the areas of the two parts = one-fifth of the average of the two areas
=> 2x - 700 = 70
=> 2x = 770
$\Rightarrow x = \dfrac{770}{2}= 385$
Hence, area of smaller part = (700 - x) = (700 – 385) = 315 hectares.