The cost of cultivating a square field at the rate of Rs. 160 per hectare is Rs. 1440. The cost of fencing it at 75 paise per metre is

Options

A. Rs.900
B. Rs.1800
C. Rs.360
D. Rs.810

Answer

To solve the problem step by step, we first need to find the area of the square field based on the cost of cultivation and then calculate the cost of fencing it.

### Step 1: Find the area of the square field

Given:
- Cost of cultivating the field = Rs. 1440
- Rate of cultivation = Rs. 160 per hectare

To find the area in hectares, we use the formula:

\[ \text{Area (hectares)} = \frac{\text{Total Cost}}{\text{Rate per hectare}} \]

Substituting the values:

\[ \text{Area (hectares)} = \frac{1440}{160} = 9 \text{ hectares} \]

### Step 2: Convert the area from hectares to square meters

1 hectare is equal to 10,000 square meters. Therefore, to convert the area to square meters:

\[ \text{Area (sq. meters)} = 9 \text{ hectares} \times 10,000 \text{ sq. meters/hectare} = 90,000 \text{ sq. meters} \]

### Step 3: Find the length of one side of the square field

Since the field is square, the area can also be expressed as:

\[ \text{Area} = \text{side}^2 \]

Let the side of the square field be \( s \). Then:

\[ s^2 = 90,000 \]

Taking the square root of both sides:

\[ s = \sqrt{90,000} = 300 \text{ meters} \]

### Step 4: Calculate the perimeter of the square field

The perimeter \( P \) of a square is given by:

\[ P = 4 \times \text{side} \]

Substituting the value of the side:

\[ P = 4 \times 300 = 1200 \text{ meters} \]

### Step 5: Calculate the cost of fencing

Given that the cost of fencing is Rs. 0.75 (or 75 paise) per meter, we can calculate the total cost of fencing:

\[ \text{Cost of fencing} = \text{Perimeter} \times \text{Cost per meter} \]

Substituting the values:

\[ \text{Cost of fencing} = 1200 \text{ meters} \times 0.75 \text{ Rs/meter} = 900 \text{ Rs} \]

### Final Answer

The cost of fencing the square field is Rs. 900.

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