Question

The length and breadth of a park are in the ratio 2:1 and its perimeter is 240m.A path 2m wide runs inside it,along its boundary.Find the cost of paving the path at Rs.80 per m2.


ANSWER IS Rs.37120 BUT I DONT KNOW THE SOLUTION.

Answer 1

Ratio of length: breadth= 2:1
Let the common multiple be x.

Length = 2x
Breadth= x.

Perimeter = 2(l+b)
240 = 2*(2x+x)
240 = 6x
x = 40
So
Length = 2*40 = 80m
Breadth = 1*40 = 40 m

Now,
As the path runs around the park so there forms an inner rectangle.

So,
the length of the Park = 80-(2+2) = 76 m
Breadth becomes = 40-(2+2) = 36 m

So now,
Area of the path = Area of the whole park - Area of the inner rectangle that has been formed
= 80*40 - 76*36
= 3200 - 2736
= 464 m^2

Now the rate of paving the path = rupees 80/m^2

Cost of paving = Rate of paving * Area of the path
= 464 * 80
= rupees 37120.

So the cost is 37120.

Hope you understood it now and received the help you needed !!!