Question

Brijbhushan is a micro financier who lends to farmers at the rate of Rs. 10 per square meter and charges 10% annual interest. Five farmers Aditya, Bhushan, Chuttan, Damodar and Govind have rectangular lands with maximum and minimum area of 10{,}000 sq m and 1{,}000 sq m respectively. Damodar's land has perimeter 250 m and the ratio of length to breadth is 4:1. Area of Aditya is thrice that of Govind, while area of Aditya is the average of the areas of Damodar and Govind. Breadth of the lands of Aditya, Bhushan and Damodar is the same, while the length of Bhushan is the sum of the lengths of Aditya and Damodar.
If the width of Aditya’s land is 25 m, what is the minimum possible length of the land of Bhushan?

Hint:

For minimum value problems, always assign the minimum permissible area first and then apply structural constraints.

Answer 1

Correct Answer: 140

Step 1: Use Damodar’s dimensions.
From earlier results:
Damodar’s length \( = 100 \) m
Damodar’s breadth \( = 25 \) m
Step 2: Use common breadth condition.
Breadth of Aditya, Bhushan and Damodar is same.
So, breadth \( = 25 \) m for all three.
Step 3: Find minimum possible area of Aditya.
Minimum area allowed \( = 1000 \) sq m
So,
\[ \text{Length of Aditya} = \frac{1000}{25} = 40 \text{ m} \]
Step 4: Find Bhushan’s length.
Given:
Length of Bhushan \( = \) Length of Aditya \( + \) Length of Damodar
\[ = 40 + 100 = 140 \text{ m} \]
Step 5: Check area constraint for Bhushan.
Area of Bhushan \( = 140 \times 25 = 3500 \) sq m
Which satisfies the minimum area condition.
Thus, the minimum possible length of Bhushan’s land is \(140\) m.
Final Answer:
\[ \boxed{140 \text{ m}} \]