Question

The cost of cultivating a rectangular field at Rs 35 per square metre is Rs 71400. If the width of the field is 40 m, find its length. Also, find the cost of fencing the field at Rs 50 per metre.

Answer 1

Total cost of cultivating the field = Rs 71400
Rate of cultivating the field = Rs 35/m²


$\mathrm{Are}a\mathrm{of}\mathrm{the}\mathrm{field}=\frac{\mathrm{Total}\mathrm{cost}\mathrm{of}\mathrm{cultivating}\mathrm{the}\mathrm{field}}{\mathrm{Rate}\mathrm{of}\mathrm{cultivating}}=\frac{\mathrm{Rs}71400}{\mathrm{Rs}35/{\mathrm{m}}^2}=2040{\mathrm{m}}^2$

Let the length of the field be x m.

$$\begin{gathered} \mathrm{Area}\mathrm{of}the\mathrm{field}=(L\mathrm{ength}\times W\mathrm{idth}){\mathrm{m}}^2=(\mathrm{x}\times 40){\mathrm{m}}^2=40\mathrm{x}{\mathrm{m}}^2 \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{field}is2040{\mathrm{m}}^2. \\ \Rightarrow 40\mathrm{x}=2040 \\ \Rightarrow \mathrm{x}=\frac{2040}{40}=51 \\ \therefore L\mathrm{ength}\mathrm{of}\mathrm{the}\mathrm{field}=51\mathrm{m} \end{gathered}$$

Perimeter of the field = 2(l+b)
= 2(51+40) m
= 182 m
Cost of fencing 1 m of the field = Rs 50
Cost of fencing 182 m of the field = Rs (182$\times$50)
= Rs 9100