The cost of wall-to-wall carpeting of the floor of a room is ₹ 24,000. If the room is 20 m long and the carpet costs ₹ 100 per sq. m, find the breadth of the room.

Answer

To solve the problem step by step, we need to find the breadth of the room given the cost of carpeting, the length of the room, and the cost per square meter of the carpet.

### Step 1: Understand the relationship between cost, area, and cost per square meter.
The total cost of carpeting the floor can be calculated using the formula:
\[ \text{Total Cost} = \text{Area} \times \text{Cost per square meter} \]

### Step 2: Substitute the given values into the formula.
From the problem, we know:
- Total Cost = ₹ 24,000
- Cost per square meter = ₹ 100

Substituting these values into the formula gives:
\[ 24,000 = \text{Area} \times 100 \]

### Step 3: Solve for the area of the room.
To find the area, we can rearrange the equation:
\[ \text{Area} = \frac{24,000}{100} \]
Calculating this gives:
\[ \text{Area} = 240 \text{ square meters} \]

### Step 4: Use the area to find the breadth of the room.
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
We know the length of the room is 20 meters, and we need to find the breadth (let's denote it as \( b \)):
\[ 240 = 20 \times b \]

### Step 5: Solve for the breadth \( b \).
Rearranging the equation to find \( b \):
\[ b = \frac{240}{20} \]
Calculating this gives:
\[ b = 12 \text{ meters} \]

### Final Answer:
The breadth of the room is **12 meters**.

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