The length, breadth and height of a room are X, Y and Z feet respectively. The cost of whitewashing the four walls of this room is Rs.2500. Find the cost of preparing another room whose length, breadth and height are double that of the previous room.

Options

A. 5000
B. 12500
C. 10000
D. 20000

Answer

To solve the problem step by step, we will first calculate the area of the four walls of the first room and then determine the cost of whitewashing the second room, which has dimensions that are double those of the first room.

### Step 1: Calculate the area of the four walls of the first room.

The formula for the area of the four walls of a room is given by:
\[ \text{Area} = 2 \times \text{Height} \times (\text{Length} + \text{Breadth}) \]
For the first room:
- Length = \(X\) feet
- Breadth = \(Y\) feet
- Height = \(Z\) feet

Substituting these values into the formula:
\[ \text{Area of the first room} = 2 \times Z \times (X + Y) \]

### Step 2: Calculate the area of the four walls of the second room.

The dimensions of the second room are double those of the first room:
- Length = \(2X\) feet
- Breadth = \(2Y\) feet
- Height = \(2Z\) feet

Using the same formula for the area of the four walls:
\[ \text{Area of the second room} = 2 \times (2Z) \times (2X + 2Y) \]
This simplifies to:
\[ \text{Area of the second room} = 2 \times 2Z \times 2(X + Y) = 8Z(X + Y) \]

### Step 3: Determine the ratio of the areas of the two rooms.

The area of the first room is:
\[ 2Z(X + Y) \]
The area of the second room is:
\[ 8Z(X + Y) \]
Now, we can find the ratio of the areas:
\[ \text{Ratio of areas} = \frac{8Z(X + Y)}{2Z(X + Y)} = \frac{8}{2} = 4 \]
This means the area of the second room is 4 times that of the first room.

### Step 4: Determine the cost of whitewashing the second room.

The cost of whitewashing the first room is given as Rs. 2500. Since the ratio of the areas is 4:1, the cost of whitewashing the second room will also be 4 times that of the first room:
\[ \text{Cost for the second room} = 4 \times 2500 = 10000 \]

### Final Answer:
The cost of preparing the second room is Rs. 10,000.

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