The length of a hall is 18 m and its width is 13.5 m. Find the least number of square tiles, each of side 25 cm, required to cover the floor of the hall,
(i) without leaving any margin.
(ii) leaving a margin of width 1.5 m all around.
In each case, find the cost of the tiles required at the rate of Rs. 6 per tile.

Answer

To solve the problem step by step, we will calculate the number of tiles required to cover the hall's floor in two scenarios: (i) without leaving any margin and (ii) leaving a margin of 1.5 m all around. We will also find the cost of the tiles in each case.

### Step 1: Convert the dimensions of the tile from cm to m.
- The side of each tile is given as 25 cm.
- To convert cm to m, we divide by 100:
\[ \text{Side of tile in meters} = \frac{25 \text{ cm}}{100} = 0.25 \text{ m} \]

### Step 2: Calculate the area of one tile.
- The area of a square tile is given by the formula:
\[ \text{Area of tile} = \text{side}^2 = (0.25 \text{ m})^2 = 0.0625 \text{ m}^2 \]

### Step 3: Calculate the area of the hall.
- The dimensions of the hall are given as:
- Length = 18 m
- Width = 13.5 m
- The area of the hall is:
\[ \text{Area of hall} = \text{Length} \times \text{Width} = 18 \text{ m} \times 13.5 \text{ m} = 243 \text{ m}^2 \]

### Step 4: Calculate the number of tiles required without leaving any margin.
- The number of tiles required can be calculated by dividing the area of the hall by the area of one tile:
\[ \text{Number of tiles} = \frac{\text{Area of hall}}{\text{Area of one tile}} = \frac{243 \text{ m}^2}{0.0625 \text{ m}^2} = 3888 \text{ tiles} \]

### Step 5: Calculate the cost of the tiles without margin.
- The cost of each tile is given as Rs. 6.
- The total cost is:
\[ \text{Total cost} = \text{Number of tiles} \times \text{Cost per tile} = 3888 \times 6 = 23328 \text{ Rs.} \]

### Step 6: Calculate the dimensions of the area to be covered with tiles leaving a margin of 1.5 m all around.
- The effective length and width after leaving a margin of 1.5 m on each side:
- Effective length = \(18 \text{ m} - 2 \times 1.5 \text{ m} = 15 \text{ m}\)
- Effective width = \(13.5 \text{ m} - 2 \times 1.5 \text{ m} = 10.5 \text{ m}\)

### Step 7: Calculate the area to be covered with tiles leaving a margin.
- The area to be covered is:
\[ \text{Area to be covered} = \text{Effective length} \times \text{Effective width} = 15 \text{ m} \times 10.5 \text{ m} = 157.5 \text{ m}^2 \]

### Step 8: Calculate the number of tiles required with the margin.
- The number of tiles required is:
\[ \text{Number of tiles with margin} = \frac{\text{Area to be covered}}{\text{Area of one tile}} = \frac{157.5 \text{ m}^2}{0.0625 \text{ m}^2} = 2520 \text{ tiles} \]

### Step 9: Calculate the cost of the tiles with margin.
- The total cost is:
\[ \text{Total cost with margin} = \text{Number of tiles with margin} \times \text{Cost per tile} = 2520 \times 6 = 15120 \text{ Rs.} \]

### Final Summary:
1. **Without Margin:**
- Number of tiles required: 3888
- Total cost: Rs. 23328

2. **With Margin:**
- Number of tiles required: 2520
- Total cost: Rs. 15120