Two crossing roads inside an 80 m × 60 m lawn, each 10 m wide: Find the cost of gravelling the roads at Rs 3 per sq m.
Aptitude
Area
Difficulty: Easy
Choose an option
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ARs. 3600
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BRs. 3800
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CRs. 3900
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DRs. 3700
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ENone of these
Answer
Correct Answer: Rs. 3900
Explanation
Introduction / Context:Two strips cross at right angles. Sum their areas and subtract the central overlap counted twice.
Given Data / Assumptions:
- Lawn: 80 m by 60 m.
- Road width w = 10 m.
- Rate = Rs 3 per sq m.
Concept / Approach:Road area = (80×10) + (60×10) − (10×10).
Step-by-Step Solution:
1) Lengthwise strip area = 800 sq m.2) Breadthwise strip area = 600 sq m.3) Overlap = 100 sq m.4) Total road area = 800 + 600 − 100 = 1300 sq m.5) Cost = 1300 * 3 = Rs 3900.Verification / Alternative check:Visualize two rectangles crossing; the overlap is a 10×10 square.
Why Other Options Are Wrong:3600, 3700, 3800 result from miscounting the overlap or one strip.
Common Pitfalls:Adding both strips without subtracting the overlapped square.
Final Answer:Rs. 3900.