A rectangular grassy plot is 120 m by 60 m. A gravel path of uniform width 1.5 m runs all around the inside of the plot (along the boundary). Find the total cost of gravelling this inside path at the rate of 65 paise per sq metre.

Introduction / Context:
This is a classic “path inside a rectangle” mensuration question. The gravel path occupies the area between the outer rectangle (the full plot) and the inner rectangle (the grassy region left after removing the path width from all sides). Once the path area is found, multiplying by the rate per sq metre gives the total cost. The main trick is reducing both length and breadth by twice the path width because the path is on all sides inside.

Given Data / Assumptions:

• Outer rectangle dimensions: 120 m and 60 m
• Path width inside all around: 1.5 m
• Rate = 65 paise per sq m = Rs. 0.65 per sq m

Concept / Approach:
Path area = (outer area) - (inner area). Inner dimensions = (L - 2w) and (B - 2w) because you lose w from both ends on each side. Then cost = path area * rate.

Step-by-Step Solution:
Outer area = 120*60 = 7200 sq mInner length = 120 - 2*1.5 = 120 - 3 = 117 mInner breadth = 60 - 2*1.5 = 60 - 3 = 57 mInner area = 117*57 = 6669 sq mPath area = 7200 - 6669 = 531 sq mCost = 531 * 0.65 = 345.15

Verification / Alternative check:
Another check: the path is relatively thin (1.5 m), so the area removed should be much smaller than 7200. We got 531, which is reasonable (about 7.4% of 7200). Multiplying by Rs. 0.65 should give a few hundred rupees, matching Rs. 345.15.

Why Other Options Are Wrong:
Rs. 245.10 and Rs. 234.18 arise from using wrong path area (often subtracting only once w instead of 2w). Rs. 456.65 is too high and typically results from using an outside path formula or incorrect inner area. Rs. 315.15 indicates a small arithmetic error in multiplying by 0.65 or a mistaken path area value.

Common Pitfalls:
Forgetting that the path is on all four sides (must subtract 2w from each dimension). Using 65 as rupees instead of paise. Computing perimeter instead of area. Making multiplication mistakes when finding 117*57 or 531*0.65.

Final Answer:
Rs. 345.15