What is the area of a rectangular plot? Consider the following statements: I. The perimeter of the plot is 208 metres. II. The length of the plot is greater than its breadth by 4 metres.

Introduction / Context:
This data sufficiency question is about finding the area of a rectangular plot. We are given the perimeter and a relation between length and breadth in two separate statements. The key is to determine whether either statement alone or both together allow us to compute a unique area. The question checks understanding of basic geometry formulas and how many conditions are needed to fix a rectangle dimensions.

Given Data / Assumptions:

• The plot is rectangular with length L and breadth B.
• Statement I: The perimeter of the plot is 208 metres.
• Statement II: The length is 4 metres more than the breadth, that is, L = B + 4.
• Area of a rectangle is L * B, and perimeter is 2 * (L + B).

Concept / Approach:
A rectangle is determined by two independent measurements, such as length and breadth. Perimeter alone gives only one equation relating L and B, and a simple difference relation alone also gives one equation. To compute the area uniquely, we must determine L and B. Therefore we check if each statement alone is enough to fix both dimensions, and then whether the combination is enough.

Step-by-Step Solution:
Step 1: From statement I, perimeter P is 208 metres. The formula for the perimeter of a rectangle is P = 2 * (L + B). So we have 2 * (L + B) = 208, or L + B = 104. Step 2: With statement I alone, we only know that L + B = 104. There are many pairs (L, B) that satisfy this, such as (50, 54), (40, 64), and so on. Each pair gives a different area. Therefore statement I alone is not sufficient. Step 3: From statement II, L = B + 4. This gives a difference relation between length and breadth, but no information about their sum or any absolute size. Many pairs of dimensions satisfy this relation, such as (10, 6), (20, 16), and so on. Each would result in a different area. Hence statement II alone is also not sufficient. Step 4: Combine statements I and II. We have L + B = 104 and L = B + 4. Substitute L into the sum equation: (B + 4) + B = 104. Step 5: Simplify the equation. This gives 2B + 4 = 104. Subtract 4 from both sides to obtain 2B = 100, so B = 50. Then L = B + 4 = 54. Step 6: Compute the area. Area = L * B = 54 * 50 = 2700 square metres. Because the dimensions are now uniquely determined, the area is unique as well.

Verification / Alternative check:
To verify sufficiency, note that we started with two unknowns L and B. Statement I reduced them to one free variable by giving a relation between L and B, but not a unique solution. Statement II also reduced them to one free variable by another relation. When both relations are used together, they form a system of two equations in two unknowns, which yields a unique solution. Without both equations, we always have infinitely many possible rectangles and therefore multiple possible areas.

Why Other Options Are Wrong:
Option A is wrong because perimeter alone does not fully determine the shape dimensions. Option B is wrong because knowing only the difference between length and breadth is not enough to fix their values. Option C claims that either statement alone is sufficient, which is not true. Option E claims that even both statements together are not sufficient, which contradicts the clear solution we obtained. Only option D correctly recognises that both statements together are necessary and sufficient.

Common Pitfalls:
A typical mistake is to think that a known perimeter always fixes a unique rectangle, forgetting that length and breadth can vary while keeping the same sum. Another error is to overlook basic algebra when dealing with the difference relation. Writing down the two equations explicitly and solving them step by step prevents these misunderstandings.

Final Answer:
The data in both statements I and II together are necessary to answer the question, so the correct option is D.