Question

The length of the floor if a rectangle hall is 10 m more than its breadth. If 34 carpets of size 6 × 4m are required to cover the floor of the hall, then find the breadth and length of the hall.

• A. 22, 24 M
• B. 22, 32 M
• C. 24, 34 M
• D. 24, 30 M

Hint:

To save time, check the options directly: the difference between length and breadth must be 10 m. Only (B) and (C) satisfy this. Multiply their values:
- For B: $22 \times 32 = 704 \neq 816$.
- For C: $24 \times 34 = 816$. This confirms Option (C) instantly.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The total area of the floor is equal to the cumulative area of all the carpets required to cover it.
Detailed Explanation:
Let us first find the total area of the floor:
- Area of one carpet = $6\text{ m} \times 4\text{ m} = 24\text{ m}^2$
- Number of carpets required = 34
- Total Area of the hall = $34 \times 24 = 816\text{ m}^2$
Let the breadth of the hall be $b$ meters.
The length of the hall is given as 10 m more than its breadth: \[ \text{Length } (l) = b + 10 \] Set up the area equation: \[ \text{Area} = l \times b \] \[ 816 = b(b + 10) \] \[ b^2 + 10b - 816 = 0 \] Solve the quadratic equation: \[ b^2 + 34b - 24b - 816 = 0 \] \[ b(b + 34) - 24(b + 34) = 0 \] \[ (b + 34)(b - 24) = 0 \] Since breadth cannot be negative, we have: \[ b = 24\text{ m} \] Calculate the length: \[ l = b + 10 = 24 + 10 = 34\text{ m} \] Thus, the breadth is 24 m and the length is 34 m.

Step 2: Final Answer:
The dimensions are 24 m and 34 m, matching Option (C).