Fence cost → perimeter → dimensions: The length of a rectangular plot exceeds its breadth by 20 m. If the perimeter fencing costs Rs 5300 at Rs 26.50 per metre, find the length (in metres).
Aptitude
Volume and Surface Area
Difficulty: Easy
Choose an option
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A40
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B120
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C50
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DNone of these
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E60
Answer
Correct Answer: 60
Explanation
Introduction / Context:Translate total fence cost to total perimeter, then use the linear relation between length and breadth to solve the dimensions.
Given Data / Assumptions:
- Rate = Rs 26.50/m; total cost = Rs 5300 ⇒ perimeter P = 5300/26.5 = 200 m.
- L = B + 20.
Concept / Approach:P = 2(L + B). Substitute L = B + 20 and solve for B, then get L.
Step-by-Step Solution:
1) L + B = 200/2 = 100.2) (B + 20) + B = 100 ⇒ 2B = 80 ⇒ B = 40.3) L = 40 + 20 = 60 m.Verification / Alternative check:Perimeter check: 2(60 + 40) = 200 m; multiplied by 26.5 ⇒ Rs 5300.
Why Other Options Are Wrong:40 and 50 are not the length; 120 is the sum of sides? Incorrect. “None of these” is not needed since the exact length is 60.
Common Pitfalls:Forgetting to halve the perimeter when solving L + B; mixing up which side is longer.
Final Answer:60.