A large field of 700 hectares is divided into two parts. The difference between 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?

Let, the area of larger part = x hector
∴ area of smaller part = (700 - x) hectors
The difference between the areas of the two parts
= x - (700 - x)
= 2x - 700
One-fifth of the average of the two areas
(1/5) × (700/2) [total area = 700]
= 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
⇒ x = 385.

∴ Smaller part of the land is = (700 - 385) = 315 hectares.