The cost of papering four walls of a room is Rs. 48. Each one of length, breadth and height of her room as double that of the new room. The cost of papering the walls of this new room is

Options

A. Rs. 12
B. Rs. 19
C. Rs. 38
D. Rs. 28

Answer

To solve the problem, we need to find the cost of papering the walls of a new room given that the dimensions of the new room are half that of the original room. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the dimensions of the original room
Let:
- Length of the original room = L
- Breadth of the original room = B
- Height of the original room = H

The area of the four walls of the original room can be calculated as:
\[ \text{Area} = 2 \times (L \times H) + 2 \times (B \times H) = 2H(L + B) \]

### Step 2: Cost of papering the original room
According to the problem, the cost of papering the four walls of the original room is Rs. 48. Therefore, we have:
\[ \text{Cost} = \text{Area} \times \text{Cost per unit area} \]
Let the cost per unit area be C. Thus:
\[ 2H(L + B) \times C = 48 \]

### Step 3: Determine the dimensions of the new room
The dimensions of the new room are half of those of the original room:
- Length of the new room = \( \frac{L}{2} \)
- Breadth of the new room = \( \frac{B}{2} \)
- Height of the new room = \( \frac{H}{2} \)

### Step 4: Calculate the area of the four walls of the new room
The area of the four walls of the new room can be calculated as:
\[ \text{Area}_{\text{new}} = 2 \times \left(\frac{L}{2} \times \frac{H}{2}\right) + 2 \times \left(\frac{B}{2} \times \frac{H}{2}\right) \]
\[ = 2 \times \left(\frac{LH}{4}\right) + 2 \times \left(\frac{BH}{4}\right) \]
\[ = \frac{LH}{2} + \frac{BH}{2} = \frac{H(L + B)}{2} \]

### Step 5: Relate the area of the new room to the cost
From the original room, we know:
\[ 2H(L + B) \times C = 48 \]
Thus:
\[ H(L + B) \times C = 24 \]

Now, for the new room:
\[ \text{Area}_{\text{new}} \times C = \frac{H(L + B)}{2} \times C \]
Substituting the value of \( H(L + B) \):
\[ = \frac{24}{2} = 12 \]

### Step 6: Conclusion
The cost of papering the walls of the new room is Rs. 12.