Question

The cost of harvesting a square field at ₹900 per hectare is ₹8100. Find the cost of putting a fence around it at ₹18 per metre.

Answer 1

$$\begin{gathered} \mathrm{As},\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{the}\mathrm{harvesting}=₹900\mathrm{per}\mathrm{hectare} \\ \mathrm{And},\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{harvesting}=₹8100 \\ \mathrm{So},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{square}\mathrm{field}=\frac{8100}{900}=9\mathrm{hectare} \\ \Rightarrow \mathrm{the}\mathrm{area}=90000{\mathrm{m}}^2\left(\mathrm{As},1\mathrm{hectare}=10000{\mathrm{m}}^2\right) \\ \Rightarrow {\left(\mathrm{side}\right)}^2=90000 \\ \Rightarrow \mathrm{side}=\sqrt{90000} \\ \mathrm{So},\mathrm{side}=300\mathrm{m} \\ \mathrm{Now},\mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{field}=4\times \mathrm{side} \\ =4\times 300 \\ =1200\mathrm{m} \\ \mathrm{Since},\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{putting}\mathrm{the}\mathrm{fence}=₹18\mathrm{per}\mathrm{m} \\ \mathrm{So},\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{putting}\mathrm{the}\mathrm{fence}=1200\times 18=₹21,600 \end{gathered}$$