A rectangular grassy plot `160 m xx 45 m` has a gravel path 3 m wide all the four sides inside it. Find the cost of gravelling the path at ? 5 per sq m.

Options

A. `? 5970`
B. `? 4979`
C. `? 6400`
D. `? 4970`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the area of the rectangular grassy plot.
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 160 m
- Breadth = 45 m

Calculating the area:
\[ \text{Area} = 160 \, \text{m} \times 45 \, \text{m} = 7200 \, \text{m}^2 \]

### Step 2: Determine the dimensions of the inner rectangle after the gravel path is added.
The gravel path is 3 m wide on all four sides, so we need to subtract 3 m from each side of the length and breadth.

Calculating the new dimensions:
- New Length (L') = 160 m - 3 m - 3 m = 154 m
- New Breadth (B') = 45 m - 3 m - 3 m = 39 m

### Step 3: Calculate the area of the inner rectangle.
Using the new dimensions:
\[ \text{Area of inner rectangle} = L' \times B' = 154 \, \text{m} \times 39 \, \text{m} \]

Calculating the area:
\[ \text{Area of inner rectangle} = 154 \times 39 = 6006 \, \text{m}^2 \]

### Step 4: Calculate the area of the gravel path.
The area of the gravel path can be found by subtracting the area of the inner rectangle from the area of the original rectangular plot:
\[ \text{Area of gravel path} = \text{Area of original plot} - \text{Area of inner rectangle} \]
\[ \text{Area of gravel path} = 7200 \, \text{m}^2 - 6006 \, \text{m}^2 = 1194 \, \text{m}^2 \]

### Step 5: Calculate the cost of gravelling the path.
The cost of gravelling is given as ₹5 per square meter. Therefore, the total cost can be calculated as:
\[ \text{Cost} = \text{Area of gravel path} \times \text{Cost per sq m} \]
\[ \text{Cost} = 1194 \, \text{m}^2 \times 5 \, \text{₹/m}^2 = 5970 \, \text{₹} \]

### Final Answer:
The cost of gravelling the path is ₹5970.

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