The cost of papering the four walls of a room is rs 480 . Each one of length , breadth and height of another room is double that of this room .What is the cost of papering the walls of the new room ?

Options

A. Rs 3840
B. Rs 2880
C. Rs 1920
D. Rs 960

Answer

To solve the problem step by step, we can follow these instructions:

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

### Step 2: Calculate the area of the four walls of the old room
The formula for the area of the four walls of a room is given by:
\[ \text{Area} = 2 \times \text{Height} \times (\text{Length} + \text{Breadth}) \]
So, for the old room:
\[ \text{Area}_{\text{old}} = 2 \times H \times (L + B) \]

### Step 3: Determine the cost of papering the old room
According to the problem, the cost of papering the four walls of the old room is Rs 480. Therefore, we can set up the equation:
\[ \text{Cost}_{\text{old}} = \text{Area}_{\text{old}} \times \text{Cost per unit area} \]
Let the cost per unit area be \( C \):
\[ 2 \times H \times (L + B) \times C = 480 \]

### Step 4: Understand the dimensions of the new room
The dimensions of the new room are double that of the old room:
- Length = 2L
- Breadth = 2B
- Height = 2H

### Step 5: Calculate the area of the four walls of the new room
Using the same formula for the new room:
\[ \text{Area}_{\text{new}} = 2 \times \text{Height}_{\text{new}} \times (\text{Length}_{\text{new}} + \text{Breadth}_{\text{new}}) \]
Substituting the dimensions of the new room:
\[ \text{Area}_{\text{new}} = 2 \times (2H) \times (2L + 2B) \]
This simplifies to:
\[ \text{Area}_{\text{new}} = 2 \times 2H \times 2(L + B) = 8H(L + B) \]

### Step 6: Relate the area of the new room to the old room
From the area of the old room, we know:
\[ \text{Area}_{\text{old}} = 2H(L + B) \]
Thus, we can express the area of the new room in terms of the old room:
\[ \text{Area}_{\text{new}} = 4 \times \text{Area}_{\text{old}} \]

### Step 7: Calculate the cost of papering the new room
Since the area of the new room is four times that of the old room, the cost of papering the new room will also be four times the cost of the old room:
\[ \text{Cost}_{\text{new}} = 4 \times \text{Cost}_{\text{old}} = 4 \times 480 = 1920 \]

### Final Answer
The cost of papering the walls of the new room is Rs 1920.

---