A rectangular lawn measures 55 m by 35 m. Two roads, each 4 m wide, run through the middle of the lawn: one road is parallel to the length and the other is parallel to the breadth. Find the total cost of gravelling the roads at the rate of 75 paise per sq m (that is, ₹0.75 per sq m), taking care to avoid double-counting the overlapping central area.

Introduction / Context:This question tests area calculation of intersecting strips (roads) inside a rectangle and then converts area into cost. When two roads cross at the center, simply adding their areas double-counts the overlap region. The correct approach is: area of road along length + area of road along breadth - overlapping area. Then multiply by the gravelling rate, converting paise to rupees properly.

Given Data / Assumptions:

• Lawn dimensions: 55 m by 35 m
• Two roads, each width = 4 m
• One road runs along length (55 m), other along breadth (35 m)
• Overlap area is a 4 m by 4 m square
• Rate = 75 paise per sq m = ₹0.75 per sq m

Concept / Approach:Area of strip = (length of strip) * (width). Total road area = A1 + A2 - overlap. Cost = total area * rate.

Step-by-Step Solution:

Verification / Alternative check:The combined road area must be less than 220 + 140 = 360 because the 16 sq m overlap should be removed once. 344 fits this logic. Multiplying 344 by ₹0.75 gives ₹258 exactly, which is consistent with a simple three-quarters multiplication.

Why Other Options Are Wrong:

Common Pitfalls:Common mistakes include adding areas without subtracting overlap, or using 75 as rupees instead of paise (₹75) which inflates the cost massively. Another pitfall is using 55 + 35 as length for a single road, which is conceptually wrong because there are two separate strips.

Final Answer:₹258