Gravel path inside a rectangular lawn (unit corrections applied)\nA rectangular grassy plot measures 110 m by 65 m. A 0.5 m wide gravel path runs all around the inside. Find the cost of gravelling the path at ₹0.80 per m².

Difficulty: Medium

Correct Answer: ₹139.20

Explanation:


Introduction / Context:
When a uniform path runs inside a rectangle, the path area equals outer area minus inner rectangle area. Here, obvious unit typos are interpreted reasonably (metres throughout, 0.5 m path).


Given Data / Assumptions:

  • Outer dimensions: 110 m by 65 m
  • Path width w = 0.5 m inside on all sides
  • Rate = ₹0.80 per m^2 (80 paise per m^2)


Concept / Approach:
Inner rectangle dimensions reduce by 2w in each direction. Path area = Outer − Inner.


Step-by-Step Solution:

Outer area = 110 * 65 = 7,150 m^2 Inner dimensions = (110 − 1) * (65 − 1) = 109 * 64 Inner area = 6,976 m^2 Path area = 7,150 − 6,976 = 174 m^2 Cost = 174 * 0.80 = ₹139.20


Verification / Alternative check:
Approximate path area also equals perimeter * width − 4 * (w^2) for thin paths: 2(110+65)*0.5 − 4*(0.25) = 350*0.5 − 1 = 175 − 1 = 174 m^2, same result.


Why Other Options Are Wrong:
₹340, ₹320, and ₹480 arise from misread unit rates or dimensions; only ₹139.20 matches the corrected interpretation and exact calculation.


Common Pitfalls:
Using centimetres inadvertently or treating the cost as ₹80 per m^2 instead of ₹0.80 per m^2 drastically overstates the amount.


Final Answer:
₹139.20

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