A pathway of uniform width 2 m is constructed inside a rectangular plot. The area of the original plot is 96 square metres. If the cost of construction is ₹50 per square metre, determine the total cost of constructing the pathway.

Introduction / Context:
This problem checks whether sufficient information is available to compute the area of a pathway constructed inside a rectangle. While the width of the pathway and the total area of the plot are given, the individual dimensions of the rectangle are not specified.

Given Data / Assumptions:

• Area of rectangular plot = 96 m^2
• Width of pathway = 2 m (inside the plot)
• Cost = ₹50 per m^2

Concept / Approach:
To find the area of the pathway, the dimensions of the rectangle (length and breadth) are required. Knowing only the area does not uniquely determine the shape of the rectangle, so the inner dimensions after subtracting the pathway width cannot be calculated.

Step-by-Step Solution:
Let original dimensions be l and b such that l*b = 96 Inner rectangle dimensions become (l - 4) and (b - 4) Pathway area = l*b - (l - 4)(b - 4) Without knowing l and b separately, pathway area cannot be determined uniquely

Verification / Alternative check:
Different rectangles with area 96 (for example 12x8 or 16x6) give different pathway areas, proving that the answer is not unique.

Why Other Options Are Wrong:
₹2000, ₹3000, ₹4000, ₹4800: each assumes specific dimensions not provided in the question.

Common Pitfalls:
Assuming the rectangle is a square without justification. Proceeding with calculations despite missing essential data. Ignoring that multiple rectangles can have the same area.

Final Answer:
The given data is insufficient to determine the cost