The cost of painting the four walls of a room is Rs. 350. The cost of painting a room three times in length, breadth and height respectively will be—

Options

A. Rs. 1050
B. Rs. 1400
C. Rs. 3150
D. Rs. 4200

Answer

To solve the problem step by step, we will first understand the given information and then calculate the required cost of painting the room when its dimensions are tripled.

### Step 1: Understand the Cost of Painting the Original Room
The cost of painting the four walls of the original room is given as Rs. 350.

### Step 2: Formula for the Area of Four Walls
The area of the four walls of a room can be calculated using the formula:
\[ \text{Area of four walls} = 2 \times (L + B) \times H \]
where \(L\) is the length, \(B\) is the breadth, and \(H\) is the height of the room.

### Step 3: Calculate the Area of the New Room
If the dimensions of the room (length, breadth, and height) are tripled, then the new dimensions will be:
- New Length = \(3L\)
- New Breadth = \(3B\)
- New Height = \(3H\)

The area of the four walls of the new room will be:
\[ \text{Area of four walls of new room} = 2 \times (3L + 3B) \times (3H) \]
This can be simplified as:
\[ = 2 \times 3 \times (L + B) \times 3H = 18 \times (2 \times (L + B) \times H) \]

### Step 4: Relate the Areas
Notice that the area of the four walls of the new room is 9 times the area of the four walls of the original room:
\[ \text{Area of new room} = 9 \times \text{Area of original room} \]

### Step 5: Calculate the Cost of Painting the New Room
Since the cost of painting is directly proportional to the area, the cost of painting the new room will be:
\[ \text{Cost of painting new room} = 9 \times \text{Cost of painting original room} \]
Substituting the given cost:
\[ = 9 \times 350 = 3150 \]

### Final Answer
The cost of painting the room three times in length, breadth, and height respectively will be Rs. 3150.

---