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
  • A
    Rs. 3600
  • B
    Rs. 3800
  • C
    Rs. 3900
  • D
    Rs. 3700
  • E
    None 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.

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