Painting a rectangular boundary: The length and breadth of a rectangular field are in the ratio 8:7. If painting the boundary (perimeter) costs Rs 3000 at Rs 10 per metre, find the area of the field in square metres.
Aptitude
Area
Difficulty: Medium
Choose an option
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A5600 sq.m
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B1400 sq. m
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C4400 sq.m
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D3600 sq.m
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E4900 sq.m
Answer
Correct Answer: 5600 sq.m
Explanation
Introduction / Context:Cost-per-metre on a boundary gives perimeter. With side ratio known, we can solve dimensions and compute area.
Given Data / Assumptions:
- Length : Breadth = 8 : 7
- Total cost = Rs 3000 at Rs 10 per m → Perimeter P = 3000 / 10 = 300 m
Concept / Approach:Let L = 8k, B = 7k. Then perimeter P = 2(L + B) = 2 * (15k) = 30k. Solve k from P, then area L*B.
Step-by-Step Solution:
30k = 300 → k = 10L = 80 m, B = 70 mArea = 80 * 70 = 5600 sq mVerification / Alternative check:Perimeter check: 2*(80+70) = 300 m equals the derived perimeter from cost; consistent.
Why Other Options Are Wrong:1400, 4400, 3600, 4900 do not match the product 80*70 under the given perimeter constraint.
Common Pitfalls:Using 8:7 as difference instead of ratio or forgetting to double the sum when computing perimeter.
Final Answer:5600 sq.m