Question

A field of 500 Km² is divided into two parts. The difference of the areas of two parts is 4/5 of the average of two areas. What is the area of smaller part in kilometres?

1. 350 km²
2. 150 km2
3. 225 km2
4. 300 km2
5. 275 km2

Answer 1

Correct Answer - Option 2 : 150 km2

Let the larger area be x Km² and smaller area be y Km².

⇒ x + y = 500      ----(1)

According to the question, the difference of the areas of two parts is 4/5 of the average of two areas.

⇒ (x – y) = 4/5[(x + y)/2]            

⇒ (x – y) = 2/5(x + y)      ----(2)

Put the value of  (x + y) from equation (1) in equation (2),

⇒ (x - y) = 2/5 × 500

⇒ x – y = 200      ----(3)

On solving equation (1) and (3) we get,

⇒ x = 350 Km² and y = 150 Km²        

Hence the area of smaller part is 150 Km².