Length of a room is twice its height and its breadth is `1(1)/(2)` times its height. The cost of white washing the walls at the rate of 32 per sq. m is * 3,584. Find the cost of tiling the floor of the room at 135 per sq. m.

Answer

To solve the problem step by step, we will follow the information given in the question and use the formulas for surface area and area calculations.

### Step 1: Define Variables
Let the height of the room be \( h \) meters. According to the problem:
- Length \( l = 2h \)
- Breadth \( b = \frac{3}{2}h \)

### Step 2: Calculate the Curved Surface Area (CSA) of the Room
The cost of whitewashing the walls is given as ₹3584 at the rate of ₹32 per square meter.

To find the area that was whitewashed (which is the curved surface area of the room), we can use the formula:
\[ \text{Curved Surface Area (CSA)} = 2h(l + b) \]
Substituting the values of \( l \) and \( b \):
\[ CSA = 2h(2h + \frac{3}{2}h) = 2h(\frac{4h + 3h}{2}) = 2h(\frac{7h}{2}) = 7h^2 \]

### Step 3: Calculate the Area from Cost
The total area can also be calculated from the total cost of whitewashing:
\[ \text{Area} = \frac{\text{Total Cost}}{\text{Cost per sq. m}} = \frac{3584}{32} = 112 \text{ sq. m} \]
Thus, we have:
\[ 7h^2 = 112 \]

### Step 4: Solve for Height \( h \)
Now, we can solve for \( h \):
\[ h^2 = \frac{112}{7} = 16 \]
\[ h = \sqrt{16} = 4 \text{ meters} \]

### Step 5: Calculate Length and Breadth
Now that we have \( h \):
- Length \( l = 2h = 2 \times 4 = 8 \text{ meters} \)
- Breadth \( b = \frac{3}{2}h = \frac{3}{2} \times 4 = 6 \text{ meters} \)

### Step 6: Calculate the Area of the Floor
The area of the floor (which is a rectangle) can be calculated as:
\[ \text{Area of Floor} = l \times b = 8 \times 6 = 48 \text{ sq. m} \]

### Step 7: Calculate the Cost of Tiling the Floor
The cost of tiling the floor at the rate of ₹135 per sq. m is:
\[ \text{Cost of Tiling} = \text{Area of Floor} \times \text{Cost per sq. m} = 48 \times 135 \]
Calculating this gives:
\[ \text{Cost of Tiling} = 6480 \text{ rupees} \]

### Final Answer
The cost of tiling the floor of the room is **₹6480**.

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