A room is half as long again as it is wide. The cost of carpting it at 62 paise per squre meter is `₹ 2916.48`.Find the cost of white washing the ceilling at 30 paise per meter.

Options

A. `₹2211.5`
B. `₹1114.2`
C. `₹1411.2`
D. can't be dtmind

Answer

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

### Step 1: Understand the dimensions of the room
Let the width of the room be \( w \) meters. According to the problem, the length of the room is half as long again as it is wide. This means:
\[ \text{Length} = w + \frac{1}{2}w = \frac{3}{2}w \]

### Step 2: Calculate the area of the room
The area of the room (which is the same as the area of the ceiling) can be calculated using the formula for the area of a rectangle:
\[ \text{Area} = \text{Length} \times \text{Width} = \left(\frac{3}{2}w\right) \times w = \frac{3}{2}w^2 \]

### Step 3: Find the area using the cost of carpeting
We know the cost of carpeting the room is ₹ 2916.48 at a rate of 62 paise per square meter. First, we convert the cost per square meter from paise to rupees:
\[ 62 \text{ paise} = \frac{62}{100} \text{ rupees} = 0.62 \text{ rupees} \]

Now, we can calculate the area of the room:
\[ \text{Area} = \frac{\text{Cost of carpeting}}{\text{Cost per square meter}} = \frac{2916.48}{0.62} \]

### Step 4: Perform the division to find the area
Calculating the area:
\[ \text{Area} = \frac{2916.48}{0.62} = 4704 \text{ square meters} \]

### Step 5: Calculate the cost of whitewashing the ceiling
The cost of whitewashing is given as 30 paise per square meter. We convert this to rupees:
\[ 30 \text{ paise} = \frac{30}{100} \text{ rupees} = 0.30 \text{ rupees} \]

Now, we can calculate the total cost of whitewashing the ceiling:
\[ \text{Cost of whitewashing} = \text{Area} \times \text{Cost per square meter} = 4704 \times 0.30 \]

### Step 6: Perform the multiplication to find the cost
Calculating the cost:
\[ \text{Cost of whitewashing} = 4704 \times 0.30 = 1411.20 \text{ rupees} \]

### Final Answer
The cost of whitewashing the ceiling is ₹ 1411.20.

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