2 metres broad pathway is to be constructed around a rectangular plot on the inside. The area of the plot is 96 sq. m. The rate of construction is ₹ 50 per square metre. Find the total cost of the construction.

### Concept & Area of an Inner Pathway To find the area of a path constructed on the inside of a rectangular plot, we need to know the individual dimensions of the plot or its perimeter, not just the total area. $$ \text{Area of inner path} = 2w(l + b - 2w) $$ ### Step-by-Step Solution * Let the length and breadth of the rectangular plot be $l$ and $b$. * We are given the area: $l \times b = 96$ sq. m. * The area of the 2-meter inner pathway is given by: $lb - (l - 4)(b - 4) = 4l + 4b - 16 = 4(l + b) - 16$. * To calculate this area, we need the sum of the length and breadth $(l + b)$. * Since we only have the product $lb = 96$, there are multiple possible pairs for $(l, b)$ (e.g., $12 \times 8$, $24 \times 4$, $16 \times 6$), each yielding a different perimeter and thus a different path area. * Without the perimeter or exact dimensions, the path area cannot be uniquely determined. ### Exam Strategy & Shortcut Recognize that inner/outer path area formulas depend on $(l+b)$ (perimeter). If only the product $lb$ (area) is given without a specific ratio or relationship between $l$ and $b$, the problem is generally unsolvable. ### Common Pitfall Assuming the plot is a square or guessing a specific set of dimensions (like $12 \times 8$) to force an answer. ### Final Answer Therefore, the correct answer is **Data inadequate**.