Two crossing roads inside an 80 m × 60 m lawn, each 10 m wide:\nFind the cost of gravelling the roads at Rs 3 per sq m.

Difficulty: Easy

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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