#### Question

The cost of fencing a square field at 60 paise per metre is Rs 1200. Find the cost of reaping the field at the rate of 50 paise per 100 sq. metres.

#### Solution

Given:

Cost of fencing 1 metre of a square field = 60 paise

And, the total cost of fencing the entire field = Rs 1200 = 1,20,000 paise

\[\therefore\text{ Perimeter of the square field }=\frac{120000}{60} = 2000\text{ metres }\]

\[\text{ Now, perimeter of a square }= 4\times \text{ side }\]

For the given square field:

\[4\times \text{ Side }= 2000 m\]

\[\text{ Side }=\frac{2000}{4} = 500\text{ metres }\]

\[ \therefore A {\text{ rea of the square field }= 500\times500=250000 m}^2 \]

\[ {\text{ Again, given: Cost of reaping per }100 m}^2 = 50 \text{ paise }\]

\[ \therefore {\text{ Cost of reaping per 1 m }}^2 = \frac{50}{100}\text{ paise }\]

\[ \therefore {\text{ Cost of reaping }250000 m}^2 = \frac{50}{100} \times 250000 = 125000\text{ paise }\]

Thus, the total cost of reaping the complete square field is 125000 paise, i.e. Rs 1250.