The cost of flooring a rectangular room is Rs. 5698. The rate of flooring is Rs. 37 per square metre. If the room is 14 metres long, what is the breadth of the room?

Options

A. 10m
B. 11 m
C. 13 m
D. 12 m

Answer

To find the breadth of the rectangular room, we can follow these steps:

### Step 1: Understand the relationship between cost, area, and rate
The total cost of flooring a room is given by the formula:
\[ \text{Cost} = \text{Area} \times \text{Rate} \]

### Step 2: Set up the known values
We know:
- Cost of flooring = Rs. 5698
- Rate of flooring = Rs. 37 per square metre
- Length of the room = 14 metres
- Let the breadth of the room be \( B \) metres.

### Step 3: Calculate the area of the room
The area \( A \) of the rectangular room can be calculated as:
\[ A = \text{Length} \times \text{Breadth} = 14 \times B \]

### Step 4: Substitute the area into the cost formula
Using the cost formula:
\[ 5698 = (14 \times B) \times 37 \]

### Step 5: Simplify the equation
Now, we can simplify the equation:
\[ 5698 = 518B \]
(where \( 518 = 14 \times 37 \))

### Step 6: Solve for \( B \)
To find \( B \), divide both sides by 518:
\[ B = \frac{5698}{518} \]

### Step 7: Perform the division
Calculating the division:
\[ B = 11 \]

### Conclusion
The breadth of the room is \( 11 \) metres.

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