The cost of fencing a square field at Rs.16 per metre is Rs.32000.Find the cost of  reaping the field at Rs.35 per `100m^(2)`.

Options

A. Rs. 97500
B. Rs. 86500
C. Rs. 87500
D. Rs. 77500

Answer

To solve the problem step by step, we will follow the given information and use the appropriate formulas.

### Step 1: Find the Perimeter of the Square Field
The cost of fencing the square field is given as Rs. 32,000, and the cost per meter of fencing is Rs. 16.

To find the perimeter (P) of the square field, we use the formula:
\[ P = \frac{\text{Total Cost of Fencing}}{\text{Cost per Meter}} \]

Substituting the values:
\[ P = \frac{32000}{16} = 2000 \text{ meters} \]

### Step 2: Find the Length of One Side of the Square Field
The perimeter of a square is given by the formula:
\[ P = 4 \times \text{Side} \]

Let the side of the square field be \( s \). Therefore,
\[ 2000 = 4s \]

To find \( s \):
\[ s = \frac{2000}{4} = 500 \text{ meters} \]

### Step 3: Calculate the Area of the Square Field
The area (A) of a square is calculated using the formula:
\[ A = \text{Side}^2 \]

Substituting the value of the side:
\[ A = 500^2 = 250000 \text{ square meters} \]

### Step 4: Find the Cost of Reaping the Field
The cost of reaping is given as Rs. 35 per 100 square meters.

First, we find the cost per square meter:
\[ \text{Cost per square meter} = \frac{35}{100} = 0.35 \text{ Rs/m}^2 \]

Now, to find the total cost of reaping the entire area:
\[ \text{Total Cost of Reaping} = \text{Area} \times \text{Cost per square meter} \]
\[ \text{Total Cost of Reaping} = 250000 \times 0.35 \]

Calculating the total cost:
\[ \text{Total Cost of Reaping} = 87500 \text{ Rs} \]

### Final Answer
The cost of reaping the field is Rs. 87,500.

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