A room is 5 m long and 4 m wide. A carpet has to be placed in the centre of the room, leaving 25 cm wide bare strip of floor all around the carpet. If the carpet costs ₹ 2000 per square metre, find the cost of the carpet.

Answer

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

### Step 1: Understand the dimensions of the room
The room is given as:
- Length = 5 m
- Width = 4 m

### Step 2: Convert the width of the bare strip from centimeters to meters
The bare strip around the carpet is 25 cm wide. To convert this to meters:
- 25 cm = 25/100 m = 0.25 m

### Step 3: Calculate the dimensions of the carpet
Since there is a 0.25 m strip around the carpet, we need to subtract this from both the length and width of the room:
- Length of the carpet = Length of the room - 2 * width of the strip
- Length of the carpet = 5 m - 2 * 0.25 m = 5 m - 0.5 m = 4.5 m
- Width of the carpet = Width of the room - 2 * width of the strip
- Width of the carpet = 4 m - 2 * 0.25 m = 4 m - 0.5 m = 3.5 m

### Step 4: Calculate the area of the carpet
The area of a rectangle is calculated by multiplying the length by the width:
- Area of the carpet = Length of the carpet * Width of the carpet
- Area = 4.5 m * 3.5 m = 15.75 m²

### Step 5: Calculate the cost of the carpet
The cost of the carpet is given as ₹ 2000 per square meter. Therefore, the total cost can be calculated as:
- Cost of the carpet = Area of the carpet * Cost per square meter
- Cost = 15.75 m² * ₹ 2000/m² = ₹ 31500

### Final Answer
The cost of the carpet is ₹ 31,500.

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