A room is 14.4 m long and 6.4 m wide. Its floor is to be covered with rectangular tiles of size 24 cm by 16 cm. Find the total cost of tiles at Rs. 15 per tile. 

Options

A. Rs. 26000
B. Rs. 2400
C. Rs. 36000
D. Rs. 32000

Answer

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

### Step 1: Calculate the area of the floor
The area of the floor can be calculated using the formula for the area of a rectangle, which is:
\[ \text{Area} = \text{Length} \times \text{Width} \]

Given:
- Length of the room = 14.4 m
- Width of the room = 6.4 m

Calculating the area:
\[ \text{Area of the floor} = 14.4 \, \text{m} \times 6.4 \, \text{m} \]
\[ \text{Area of the floor} = 92.16 \, \text{m}^2 \]

### Step 2: Calculate the area of one tile
The area of one tile can be calculated using the same formula for the area of a rectangle.

Given:
- Length of the tile = 24 cm = 0.24 m (since 1 cm = 0.01 m)
- Width of the tile = 16 cm = 0.16 m

Calculating the area:
\[ \text{Area of one tile} = 0.24 \, \text{m} \times 0.16 \, \text{m} \]
\[ \text{Area of one tile} = 0.0384 \, \text{m}^2 \]

### Step 3: Calculate the number of tiles required
To find the number of tiles needed, divide the total area of the floor by the area of one tile:
\[ \text{Number of tiles} = \frac{\text{Area of the floor}}{\text{Area of one tile}} \]

Calculating the number of tiles:
\[ \text{Number of tiles} = \frac{92.16 \, \text{m}^2}{0.0384 \, \text{m}^2} \]
\[ \text{Number of tiles} = 2400 \, \text{tiles} \]

### Step 4: Calculate the total cost of the tiles
The total cost can be calculated by multiplying the number of tiles by the cost per tile.

Given:
- Cost per tile = Rs. 15

Calculating the total cost:
\[ \text{Total Cost} = \text{Number of tiles} \times \text{Cost per tile} \]
\[ \text{Total Cost} = 2400 \, \text{tiles} \times 15 \, \text{Rs/tile} \]
\[ \text{Total Cost} = 36000 \, \text{Rs} \]

### Final Answer
The total cost of the tiles is Rs. 36,000.

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