The circumference of a circular park is 314 m. A 20 m. wide concrete track runsround it. Calculate the cost of laying turf in the park at Rs1.25 persq.m. and the cost of concrete track at Rs 1.25 per sq. m.

Let the radius of park including track (i.e. outside circle) be 'r ₁ ' and radius of park without including (i.e. inner circle) track be 'r ₂ '.
Given,

Circumference of Park = 314 m

we know that,

circumference of a circle = 2πr

where 'r' is the radius of the circle.

⇒ 2πr ₁ = 314

⇒ 2 × 3.14 × r ₁ = 314

⇒ 2r ₁ = 100 m

⇒ r ₁ = 50 m

Also, area of circle = πr ² , where 'r' is the radius of circle.

⇒ area of outer circle = πr ₁ ² = 3.14 × (50) ² = 7850 m ² [1]

Also,

Radius of park excluding the track, r ₂ = r ₁ - width of track = 50 - 20 = 30 m

⇒ area of inner circle = πr ₂ ² = 3.14 × (30) ² = 2826 m ²

Now,

Area of laying turf in the park = area of inner circle = 2826 m ²

Cost of laying 1 m ² = 1.25 Rs

⇒ Cost of laying 2826 m ² = 2826(1.25) = 3532.5 Rs

Also,

Area of track = Area of outer circle - Area of inner circle

⇒ Area of track = 7850 - 2826 = 5024 m ²

Cost of concrete 1 m ² of track = 1.25 Rs

Cost of concrete 5024 m ² of track = 5024(1.25) = 6280 Rs