Question

The cost of planting grass in a circular park at the rate of Rs 4.90/m2 is Rs 24, 640. A path of uniform width runs around the park. The cost of gravelling the path at the rate of rs 3.50/m2 is Rs 3696. Find the cost of fencing the path on both sides at the rate of Rs 2.10/m

Answer 1

Answer:

Rs 1108.8

Step-by-step explanation:

The cost of planting grass in a circular park at the rate of Rs 4.90/m2 is Rs 24, 640. A path of uniform width runs around the park. The cost of gravelling the path at the rate of rs 3.50/m2 is Rs 3696. Find the cost of fencing the path on both sides at the rate of Rs 2.10/m

Answer :

Its a circular field & uniform path around the park

Let say Radius of inner Park = R  m

Let say width of Path = X m

Radius of park including Path = R + X m

Area of a Park = $\pi \times R^2$ m²  

Value of $\pi = \frac{22}{7}$

Area of a Park = (22/7) × R²  m²

Cost of Planting Grass = Rs 4.9 /m²

Cost of Planting grass in Park = 4.9 × (22/7) × R²  Rs

As cost of planting Grass is given = Rs 24640

=> 4.9 × (22/7) × R² = 24640

=> R² = 246400 / ( 7 × 22)

=> R² = 1600

=> R = 40

Radius of inner Park = 40 m

Area of Path = Area of Outer circle - Area of Inner Circle

=> Area of Path = (22/7) × (40 + X)² - (22/7) × 40²

=> Area of Path = (22/7) × (1600 + X² + 80X - 1600)

=> Area of Path = (22/7) × (X² + 80X)

Cost of Graveling the path = Rs 3.5 /m²

Cost of Graveling The path =  3.5 × (22/7) × (X² + 80X)

= 11 × (X² + 80X)

cost of graveling the path is given = 3696

=> 11 × (X² + 80X) = 3696

=> X² + 80X = 336

=> X² + 80X - 336 = 0

=> X² + 84X - 4X - 336 = 0

=> X (X + 84) - 4(X +84) = 0

=> (X-4)(X+84) = 0

=> X = 4  as X can not be negative

Width Of Path = 4 m

Inner radius = 40 m

Outer Radius = 40 + 4 = 44 m

Inner circumference = 2 × (22/7) × 40 = 44 × 40/7   m

Outer circumference = 2 × (22/7) × 44 = 44 × 44/7   m

As fencing need to be done both side

so total to be fenced = 44 × 40/7   +   44 × 44/7

= 44 × (40 + 44) /7

= 44 × 84/7

= 44 × 12

= 528 m

Cost Of fencing the path = Rs 2.1 m

Total  cost of Fencing = 2.1 × 528 =  Rs 1108.8

Answer 2

Step-by-step explanation:

Rs 1108.8

Step-by-step explanation:

The cost of planting grass in a circular park at the rate of Rs 4.90/m2 is Rs 24, 640. A path of uniform width runs around the park. The cost of gravelling the path at the rate of rs 3.50/m2 is Rs 3696. Find the cost of fencing the path on both sides at the rate of Rs 2.10/m

Answer :

Its a circular field & uniform path around the park

Let say Radius of inner Park = R m

Let say width of Path = X m

Radius of park including Path = R + X m

Area of a Park = \pi \times R^2π×R

2

m²

Value of \pi = \frac{22}{7}π=

7

22

Area of a Park = (22/7) × R² m²

Cost of Planting Grass = Rs 4.9 /m²

Cost of Planting grass in Park = 4.9 × (22/7) × R² Rs

As cost of planting Grass is given = Rs 24640

=> 4.9 × (22/7) × R² = 24640

=> R² = 246400 / ( 7 × 22)

=> R² = 1600

=> R = 40

Radius of inner Park = 40 m

Area of Path = Area of Outer circle - Area of Inner Circle

=> Area of Path = (22/7) × (40 + X)² - (22/7) × 40²

=> Area of Path = (22/7) × (1600 + X² + 80X - 1600)

=> Area of Path = (22/7) × (X² + 80X)

Cost of Graveling the path = Rs 3.5 /m²

Cost of Graveling The path = 3.5 × (22/7) × (X² + 80X)

= 11 × (X² + 80X)

cost of graveling the path is given = 3696

=> 11 × (X² + 80X) = 3696

=> X² + 80X = 336

=> X² + 80X - 336 = 0

=> X² + 84X - 4X - 336 = 0

=> X (X + 84) - 4(X +84) = 0

=> (X-4)(X+84) = 0

=> X = 4 as X can not be negative

Width Of Path = 4 m

Inner radius = 40 m

Outer Radius = 40 + 4 = 44 m

Inner circumference = 2 × (22/7) × 40 = 44 × 40/7 m

Outer circumference = 2 × (22/7) × 44 = 44 × 44/7 m

As fencing need to be done both side

so total to be fenced = 44 × 40/7 + 44 × 44/7

= 44 × (40 + 44) /7

= 44 × 84/7

= 44 × 12

= 528 m

Cost Of fencing the path = Rs 2.1 m

Total cost of Fencing = 2.1 × 528 = Rs 1108.8