Lawn 120 m × 60 m with 1.5 m inner border all around: A rectangular grassy plot 120 m by 60 m has a 1.5 m wide gravel path running all round on the inside. Find the cost of gravelling this path at Rs 0.65 per sq m.
Aptitude
Area
Difficulty: Easy
Choose an option
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ARs. 345.15
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BRs. 245.10
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CRs. 234.18
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DRs. 456.65
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ENone of these
Answer
Correct Answer: Rs. 345.15
Explanation
Introduction / Context:Border (annulus-like) area equals outer rectangle minus the inner clear rectangle after shrinking each side by twice the border width.
Given Data / Assumptions:
- Outer: 120 m × 60 m.
- Border width w = 1.5 m.
- Rate = Rs 0.65 per sq m.
Concept / Approach:Inner dimensions = (120 − 2w) × (60 − 2w) = 117 × 57. Area(path) = 120×60 − 117×57.
Step-by-Step Solution:
1) Outer area = 7200 sq m.2) Inner area = 117 × 57 = 6669 sq m.3) Path area = 7200 − 6669 = 531 sq m.4) Cost = 531 × 0.65 = Rs 345.15.Verification / Alternative check:Difference-of-areas method is standard for uniform borders.
Why Other Options Are Wrong:They correspond to incorrect inner dimensions or rate multiplication.
Common Pitfalls:Subtracting only once the width instead of twice (both sides).
Final Answer:Rs. 345.15.