Question

in figure a path 2.5 m wide runs along inside the boundary of a square fields whose side is 65 metre the path is to be covered with red gravel and the rest of the field to be manured. find the total expenses involve if the cost of covering the path with red gravel is rupees 1.50 per metre square and that of manuring the field rupees 0.50metre square​

Answer 1

Given :

Side of square field :

= 65 m

Width of inside path:

= 2.5 m

Cost for the covering the path with red gravel :

= Rs 1.50  per square m

Cost of manuring the field :

=Rs 0.50 per square m

To Find :

The total cost involved =?

Solution:

∴Side of square field is :

= 65 m  

And the path inside it is of width :

= 2.5 m

So the side of field to be manured is :

=(65- 2.5 ) m

= 62.5 m

⇒Therefore of the field to be manured :

$=62.5^{2} m^{2} \\=3906.25 m^{2}$

Now the area of the inside path to be covered with red gravel :

$= 4\times (65\times 2.5) - 4\times 2.5^{2} \\=650 - 25\\=625 m^{2}$

So  the cost of covering path with red gravel :

$=Rs 1.50\times 625\\\\=Rs 781.25$

And the cost of manuring the field :

$=Rs o.50\times 3906.25\\=Rs 1953.125$

Therefore the total cost :

= Rs 1953.125 + 781.25

=Rs 2734.375