Question

What is the rate per metre length of the fencing of the rectangular field? I) The area of the field is \(10,000\) sq. metres.
II) The total cost for fencing the field is Rs. \(1,00,000\).

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question
• C. Both the statements I and II are sufficient to answer the question but neither statement alone is not sufficient
• D. Both the statements I and II together are not sufficient to answer the question and additional data is required

Hint:

For fencing rate, perimeter is required. Area alone cannot determine the perimeter of a rectangle.

Answer 1

The Correct Option is D

Concept:
The rate per metre of fencing is calculated by \[ \text{Rate per metre}=\frac{\text{Total cost}}{\text{Total length of fencing}} \] For a rectangular field, total length of fencing is its perimeter: \[ \text{Perimeter}=2(l+b) \]

Step 1: Check Statement I. Statement I gives only the area: \[ lb=10000 \] But from area alone, we cannot find the perimeter. For example, many rectangles can have area \(10000\) but different perimeters. So Statement I alone is not sufficient.

Step 2: Check Statement II. Statement II gives only total cost: \[ \text{Total cost}=100000 \] But the fencing length is unknown. So Statement II alone is not sufficient.

Step 3: Combine both statements. Even using both statements, we know: \[ lb=10000 \] and \[ \text{Total cost}=100000 \] But we still do not know \(l+b\), so we cannot determine the perimeter. Therefore, the rate per metre cannot be determined.

Step 4: Final answer. \[ \boxed{\text{Both statements together are not sufficient}} \]