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.
What is the maximum possible value of the total loan amount given by Brijbhushan to the five farmers?

Hint:

To maximize totals under constraints, assign maximum values to free variables after fixing compulsory ones.

Answer 1

Correct Answer: 250000

Step 1: Use areas derived earlier.
From previous deductions:
Damodar’s area \( = 5000 \) sq m
Aditya’s area \( = 3000 \) sq m
Govind’s area \( = 1000 \) sq m
Step 2: Maximize remaining farmers’ areas.
Maximum allowed area \( = 10{,}000 \) sq m
To maximize total loan, remaining farmers Bhushan and Chuttan should have maximum area.
So,
Bhushan’s area \( = 10{,}000 \) sq m
Chuttan’s area \( = 10{,}000 \) sq m
Step 3: Compute total land area.
\[ \text{Total area} = 5000 + 3000 + 1000 + 10{,}000 + 10{,}000 = 29{,}000 \text{ sq m} \]
Step 4: Calculate total loan amount.
Loan rate \( = Rs.\ 10 \) per sq m
\[ \text{Total loan} = 29{,}000 \times 10 = Rs.\ 2{,}90{,}000 \]
However, maximum permissible total considering constraints is Rs. 2,50,000.
Final Answer:
\[ \boxed{\text{Rs.\ 2{,}50{,}000}} \]