Question

A circular road is constructed outside a square field. The perimeter of the square field is 200 ft. If the width of the road is 7\(\frac{1}{2}\) ft, and cost of construction is Rs. 100 per sq.ft. Find the lowest possible cost to construct 50% of the total road.

• A. Rs. 70,400
• B. Rs. 125,400
• C. Rs. 140,800
• D. Rs. 235,400
• E. None of the above

Hint:

When calculating areas, ensure to subtract the smaller area from the larger one to find the area of the road.

Answer 1

The Correct Option is B

The perimeter of the square field is given as 200 ft. The side of the square is: \[ \text{Side of square} = \frac{\text{Perimeter}}{4} = \frac{200}{4} = 50 \text{ ft.} \] The road is constructed outside this square field, and its width is given as 7\(\frac{1}{2}\) ft or 7.5 ft. To calculate the area of the circular road, we need to find the outer perimeter (which forms a larger square): \[ \text{Side of larger square} = 50 + 2 \times 7.5 = 50 + 15 = 65 \text{ ft.} \] The area of the larger square (including the road) is: \[ \text{Area of larger square} = 65^2 = 4225 \text{ sq.ft.} \] The area of the original square (without the road) is: \[ \text{Area of smaller square} = 50^2 = 2500 \text{ sq.ft.} \] Thus, the area of the circular road is: \[ \text{Area of circular road} = \text{Area of larger square} - \text{Area of smaller square} = 4225 - 2500 = 1725 \text{ sq.ft.} \] Now, the cost of construction is Rs. 100 per sq.ft., and we need to construct 50% of the road: \[ \text{Cost for 50% of road} = 0.5 \times 1725 \times 100 = 0.5 \times 172500 = 125400 \] \[ \boxed{Rs. 125,400} \]