The rate for a 1.20 m wide carpet is Rs 40 per metre, find the cost of covering a hall 45 m long and 32 m wide with this carpet. Also, find the cost of carpeting the same hall if the carpet, 80 cm wide, is at Rs 25 per metre.

Answer

To solve the problem, we need to calculate the cost of carpeting a hall with two different carpet widths. Let's break it down step by step.

### Step 1: Calculate the area of the hall
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Here, the length of the hall is 45 m and the width is 32 m.

\[ \text{Area} = 45 \, \text{m} \times 32 \, \text{m} = 1440 \, \text{m}^2 \]

### Step 2: Calculate the length of carpet needed for the first case
The width of the carpet is 1.20 m. To find the length of carpet needed, we can use the formula for the area of the carpet:
\[ \text{Area of carpet} = \text{Length of carpet} \times \text{Width of carpet} \]
We rearrange this to find the length of the carpet:
\[ \text{Length of carpet} = \frac{\text{Area of hall}}{\text{Width of carpet}} = \frac{1440 \, \text{m}^2}{1.20 \, \text{m}} = 1200 \, \text{m} \]

### Step 3: Calculate the cost of carpeting with the first carpet
The cost per meter for the 1.20 m wide carpet is Rs 40. Therefore, the total cost is:
\[ \text{Total cost} = \text{Length of carpet} \times \text{Cost per meter} = 1200 \, \text{m} \times 40 \, \text{Rs/m} = 48000 \, \text{Rs} \]

### Step 4: Calculate the length of carpet needed for the second case
In the second case, the width of the carpet is 80 cm, which is equal to 0.80 m. We will again use the area of the hall to find the length of carpet needed:
\[ \text{Length of carpet} = \frac{\text{Area of hall}}{\text{Width of carpet}} = \frac{1440 \, \text{m}^2}{0.80 \, \text{m}} = 1800 \, \text{m} \]

### Step 5: Calculate the cost of carpeting with the second carpet
The cost per meter for the 0.80 m wide carpet is Rs 25. Therefore, the total cost is:
\[ \text{Total cost} = \text{Length of carpet} \times \text{Cost per meter} = 1800 \, \text{m} \times 25 \, \text{Rs/m} = 45000 \, \text{Rs} \]

### Final Answers
- The cost of carpeting the hall with a 1.20 m wide carpet is Rs 48,000.
- The cost of carpeting the hall with an 0.80 m wide carpet is Rs 45,000.