Question

There is a field whose each side is 40 m. A square flower bed is prepared in its centre leaving a gravel path all around the flower bed. The total cost of laying the flower bed and gravelling the path at ₹ 1.50 and 60 paise per square meter is ₹ 2126.40. Find the length of the gravel path.

Answer 1

Given: There is a square field with side 40 m. A square flower bed is prepared in its centre leaving a gravel path all around the bed. Cost of laying the flower bed = ₹ 1.50 per m²; cost of gravelling the path = 60 paise (₹ 0.60) per m². Total cost = ₹ 2126.40.

Step-wise calculation:

1. Let the side of the square flower bed = s m.

Then the width of the gravel path = x = `(40 - s)/2` (m).

2. Area of whole field = 40² = 1600 m². 

Area of flower bed = s².

Area of path = 1600 – s².

3. Total cost = (cost for bed) + (cost for path)

= 1.50 · s² + 0.60 · (1600 – s²) 

= 2126.40

4. Simplify:

(1.50 – 0.60) s² + 0.60 · 1600 = 2126.40

⇒ 0.90 s² + 960 = 2126.40

⇒ 0.90 s² = 2126.40 – 960

⇒ 0.90 s² = 1166.40

⇒ s² = `1166.40/0.90`

⇒ s² = 1296

⇒ s = `sqrt(1296)`

⇒ s = 36 m

5. Path width x = `(40 - 36)/2`

= `4/2`

= 2 m

The gravel path is 2 metres wide.