Question

A 540 m-long rectangular plot is to be fenced. Find the cost of fencing per square metre.
I. Breadth of the plot is $60$ m.
II. Length of the plot is $120$ m.

• A. I alone sufficient; II alone not.
• B. II alone sufficient; I alone not.
• C. Either I alone or II alone sufficient.
• D. Even I + II together not sufficient.
• E. I + II together necessary.

Hint:

Check that the question's target quantity is actually computable from the variables given. Missing unit rates often make data insufficient even when dimensions are known.

Answer 1

The Correct Option is D

"540 m-long plot" indicates the total fencing required (perimeter) $=540\Rightarrow L+B=270$.
With I or II we could deduce the other dimension and hence the area; however the cost per square metre of fencing requires a price rate, which is nowhere provided. Thus even together, the data are insufficient. 

Answer 2

Notice that fencing cost is a linear-boundary cost measured per running metre, whereas the question asks for a cost per square metre, which is an area-based rate. Check what each statement, and their combination, can actually supply.

1. Option A (I alone sufficient, II not): Statement I gives the breadth, \( 60 \) m. Combined with the total fencing length \( 540 \) m, the other side could be found, but no rupee rate per unit length or area is given anywhere; the essential rate is missing. So I alone is not sufficient, and this option is rejected.
2. Option B (II alone sufficient, I not): Statement II gives the length, \( 120 \) m, similarly allowing the breadth to be deduced, but again no cost rate is supplied. So II alone is also not sufficient; rejected.
3. Option C (either alone sufficient): Since neither individually supplies a rate, this option is rejected.
4. Option D (even together not sufficient): Even combining I and II only pins down both dimensions, \( 60 \) m and \( 120 \) m, and hence the area and perimeter numerically; the rupee cost per square metre is never stated anywhere in the question or the statements, so the cost itself remains unknown regardless of how many dimensions are known. This matches.
5. Option E (I + II together necessary): This wrongly implies the combination would answer the question; since the essential rate is missing altogether, no amount of dimensional data helps, so this option is rejected.

Since a cost figure requires a rupee rate per unit area, which is never provided in the stem or either statement, the question cannot be answered no matter how many dimensions are known.

Hence, the correct answer is If even I + II together are not sufficient.