Gravel path inside a rectangular lawn (unit corrections applied) A 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.
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A₹139.20
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B₹340.00
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C₹320.00
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D₹480.00
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ENone of these
Answer
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 = ₹139.20Verification / 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