A farmer has a circular piece of land. He wishes to construct his house in the form of largest possible square within the land as shown below. The…

Area on which grass is grown = Area of two segments

\[\begin{aligned} & =2 \times\left[\frac{90}{360} \times \frac{22}{7} \times 35 \times 35-\frac{1}{2} \times 35 \times 35\right] \\ & =700 \mathrm{~m}^{2} \end{aligned} \]

Cost of growing the grass \(\displaystyle =700 \times 50=₹ 35000\)

Required ratio \(\displaystyle =\frac{\text { area of square }}{\text { area of circle-area of square }}\)

\[\begin{aligned} & =\frac{35 \sqrt{2} \times 35 \sqrt{2}}{\dfrac{22}{7} \times 35 \times 35-35 \sqrt{2} \times 35 \sqrt{2}} \\ & =\frac{2450}{1400} \text { or } \frac{7}{4} \end{aligned} \]

∴ Required ratio is $\displaystyle 7$ : $\displaystyle 4$