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Ratio of per meter fencing cost to the per square meter gardening cost is 15 : 4 and ratio of total cost of fencing to the total cost of gardening a circular field is 5 : 7, then what is the circumference of the circular field?

Ratio of per meter fencing cost to the per square meter gardening cost is 15 : 4 and ratio of total cost of fencing to the total cost of gardening a circular field is 5 : 7, then what is the circumference of the circular field? Correct Answer 66 meters

Given:

Ratio of per meter fencing cost to the per square meter gardening cost is 15 : 4

Ratio of total cost of fencing to the total cost of gardening a circular field is 5 : 7

Formula used:

Circumference of circle = 2 π r

Calculation:

Let radius of the circular field be r

Let per meter fencing cost and per square meter gardening cost be 15x and 4x respectively.

Total cost of fencing the field = 15x × 2πr = 15x × 2 × (22/7) × r = 660xr/7

Total cost of gardening the field = 4x × πr2 = 4x × (22/7) × r2 = 88xr2/7

According to the question:

(660xr/7) : (88xr2/7) = 5 : 7

r = 21/2

r = 10.5 cm

Circumference of the circular field = 2πr = 2 × (22/7) × 10.5 = 66 meters

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