Brijbhushan's Microfinance Lends

Chhuttan's plot perimeter = $2(l + w) = 250 \implies l + w = 125$. Ratio $l:w = 4:1 \implies w = 25\text{ m}, l = 100\text{ m}$. Area = $100 \times 25 = 2500\text{ m}^2$. Loan = $2500 \times 10 = \text{Rs. } 25,000$. Interest at 10% = $10\% \times 25000 = \text{Rs. } 2500$.

Let Govind's plot area = $x$. Aditya's plot area = $3x$. Average of Govind's ($x$) and Dabloo's ($y$) area = $3x \implies \frac{x+y}{2} = 3x \implies y = 5x$. Binod's plot length is sum of Aditya's and Dabloo's length (with same width) $\implies$ Binod's area = $3x + 5x = 8x$. Total area = $x (\text{Govind}) + 3x (\text{Aditya}) + 5x (\text{Dabloo}) + 8x (\text{Binod}) + 2500 (\text{Chhuttan}) = 17x + 2500$.

Maximum area for any plot is $10,000\text{ m}^2$. The largest plot is Binod's ($8x$). $8x \le 10000 \implies x \le 1250$. Maximum Total Area = $17(1250) + 2500 = 21250 + 2500 = 23750\text{ m}^2$. Maximum Total Loan = $23750 \times 10 = \text{Rs. } 237,500$.

If width $= 25\text{ m}$, then for Binod's plot, Area $= 8x$, so Length $= \frac{8x}{25}$. To minimize Binod's length, we need to minimize $x$. Minimum area of any plot is $1000\text{ m}^2$. Govind's plot has area $x$, so minimum $x = 1000$. Minimum length of Binod's plot $= \frac{8 \times 1000}{25} = 320\text{ meters}$.