A rectangular garden ($60\text{ m} \times 40\text{ m}$) is surrounded by a road of width 2 m, the road is covered by tiles and the garden is fenced. If the total expenditure is ₹ 51600 and rate of fencing is ₹ 50 per metre, then the cost of covering 1 sq. m of road by tiles is (Hotel Management, 2007)

### Concept & Cost Distribution The total expenditure comprises two distinct parts: the perimeter fencing of the inner garden and the area tiling of the outer road. Find the fencing cost first, subtract it from the total, and divide the remainder by the road area. $$ \text{Total Cost} = (\text{Perimeter} \times \text{Fencing Rate}) + (\text{Road Area} \times \text{Tiling Rate}) $$ ### Step-by-Step Solution * Given: Garden $l=60$ m, $b=40$ m. Road width $w=2$ m (outside). Total Cost = ₹ 51600. Fencing rate = ₹ 50/m. * Find fencing cost: The perimeter of the garden is $2(60 + 40) = 2(100) = 200$ m. Fencing cost = $200 \times 50 = 10000$ rupees. * Find tiling cost: Total tiling cost = Total Expenditure - Fencing Cost = $51600 - 10000 = 41600$ rupees. * Find road area: The road surrounds the garden. Outer dimensions are $(60 + 4) = 64$ m and $(40 + 4) = 44$ m. * Outer Area = $64 \times 44 = 2816\text{ m}^2$. Inner Garden Area = $60 \times 40 = 2400\text{ m}^2$. * Road Area = $2816 - 2400 = 416\text{ m}^2$. * Calculate tiling rate: Rate = Total Tiling Cost / Road Area = $41600 / 416 = 100$ rupees per sq. m. ### Exam Strategy & Shortcut To calculate the road area faster without multiplying large numbers, use the outer path formula: $\text{Area} = 2w(l + b + 2w)$. Plugging in the values: $2(2)(60 + 40 + 4) = 4(104) = 416\text{ m}^2$. Then easily compute $41600 / 416 = 100$. ### Common Pitfall Calculating the road area as an inner path instead of an outer path. "Surrounded by a road" implies the road is added outside the given garden dimensions. ### Final Answer Therefore, the correct answer is **₹ 100**.