Thelength, breadth and height of a room are in the ratio of 4 : 3 : 2. The cost of carpeting the floor at ₹ 10 per square meteris ₹ 480. The height of the room is:

Options

A. 10 m
B. 2 m
C. 6 m
D. 4 m

Answer

To solve the problem step by step, we will follow the given information and derive the height of the room.

### Step 1: Understand the Ratios
The dimensions of the room are given in the ratio of Length (L) : Breadth (B) : Height (H) = 4 : 3 : 2.

### Step 2: Assign Variables
Let’s assign variables based on the ratios:
- Length (L) = 4x
- Breadth (B) = 3x
- Height (H) = 2x

### Step 3: Calculate the Area of the Floor
The area of the floor (which is Length × Breadth) can be calculated as:
\[ \text{Area} = L \times B = (4x) \times (3x) = 12x^2 \]

### Step 4: Determine the Cost of Carpeting
We know that the cost of carpeting is ₹10 per square meter and the total cost of carpeting is ₹480.

To find the area that was carpeted, we can use the formula:
\[ \text{Area} = \frac{\text{Total Cost}}{\text{Cost per square meter}} \]
\[ \text{Area} = \frac{480}{10} = 48 \text{ square meters} \]

### Step 5: Set Up the Equation
Now, we can set the area calculated from the dimensions equal to the area we found from the cost:
\[ 12x^2 = 48 \]

### Step 6: Solve for x
To find x, we can divide both sides of the equation by 12:
\[ x^2 = \frac{48}{12} \]
\[ x^2 = 4 \]

Now, take the square root of both sides:
\[ x = \sqrt{4} \]
\[ x = 2 \]

### Step 7: Calculate the Height
Since we defined height (H) as 2x, we can now find the height:
\[ H = 2x = 2 \times 2 = 4 \text{ meters} \]

### Conclusion
The height of the room is **4 meters**.

---