Question

The cost of fencing a square field with a rate of Rs 20 per meter of Rs 10080. How much will it cost to lay a three meter wide pavement along the fencing inside the field at a rate of Rs 50 per sq meter?
(A) $Rs.70,000$
(B) $Rs.73,800$
(C) $Rs.50,000$
(D) $Rs.10,000$

Answer 1

Hint: First we will find out the perimeter of the square and after that we will require the side of the square with the help of this information we can get the cost of the pavement according to the given rate.

Complete step-by-step answer:

Given, Total cost = 10080, cost per meter = 20, find = field at rate of 50 per sq meter
First we found of perimeter,
$ \Rightarrow {\text{Perimeter = }}\dfrac{{{\text{total cost}}}}{{{\text{cost per metre}}}}$
Now we put the value of cost and cost per meter and divide both of them, we get
$
   \Rightarrow {\text{Perimeter = }}\dfrac{{{\text{10080}}}}{{{\text{20}}}} \\
   \Rightarrow {\text{Perimeter = 504m}} \\
 $
Since we have perimeter, now we will require side of square
$
   \Rightarrow {\text{side of the square = }}\dfrac{{{\text{504}}}}{{\text{4}}} \\
   \Rightarrow {\text{side of the square = 126m}} \\
 $
As the ${\text{breadth of the pavement = 3m}}$ and we take the breadth of the pavement twice because the given is one sided we consider the pavement for two sides, we get
$
   \Rightarrow {\text{breadth of the pavement = 2}} \times {\text{3m}} \\
   \Rightarrow {\text{side of inner square = 126 - 6 = 120m}} \\
 $
Now we will use the formula of area of the pavement
$ \Rightarrow {\text{area of the pavement = }}area{\text{ }}of{\text{ }}outer{\text{ }}square{\text{ }}-{\text{ }}area{\text{ }}of{\text{ }}inner{\text{ }}square$
Now putting the values in the above formula we get
$
   \Rightarrow {\text{area of the pavement = }}\left( {{\text{126 \times 126}}} \right){\text{ - }}\left( {{\text{120 \times 120}}} \right) \\
   \Rightarrow {\text{area of the pavement = 246 \times 6 = 1476}} \\
 $
Now we calculate the cost of pavement, we get
\[ \Rightarrow Cost{\text{ }}of{\text{ }}the{\text{ }}pavement{\text{ }} = 1476 \times 50\]
Now we multiply the above equation we get
\[ \Rightarrow Cost{\text{ }}of{\text{ }}the{\text{ }}pavement{\text{ }} = Rs.73800\]
So, the answer of the three metre wide pavement along the fencing inside the field at rate of 50 per sq metre is Rs.73800

Hence the correct option is B.

Note: For solving these types of questions which have inner and outer square or rectangle. First we have to find the sides of the inner and outer sides by the help of the perimeter which is given in the question. After finding the dimensions we have to find the area which is between them by subtracting both the areas here you have to remember that you have to subtract inner figure area from outer figure area.