Question

One meter of wide path is built inside a square park of 30 m along its side. The remaining part of the park is covered by grass. If the total cost of covering by grass is Rs 1176, find the rate per square meter at which the park is covered by grass.

Answer 1

Hint: The inner edge of the path will form a square. The area of the remaining part can be found by finding the area of the inner square.
Side of the inner square can be found by subtracting twice the width of the path from the side of the outer square.
Total cost = Total area $ \times $Rates per unit

Complete step by step solution:
Calculate the width of the square formed by inner edge of the path
Length of inner square = Length of outer square – 2 length of inner square
\[{\rm{S = \text{Length of outer square} - 2 }} \times {\rm{\text{Width of path}\;}}\]
  \[\begin{array}{l}
 = 30m - 2 \times 1m\\
 = 28m
\end{array}\]
Here, S is the length of the inner square.

Step 2
Express the relation of area and side of the square
\[{\rm{\text{Area of the square = side} }} \times {\rm{\text{ side}}}\]
\[\begin{array}{l}
{\rm{A = 28m}} \times {\rm{28m}}\\
{\rm{A = 784}}{{\rm{m}}^2}
\end{array}\]
Here, A is the area of the inner square.

Step 3
Express the relation of cost of covering the park with grass and area of the park
Cost of covering the area with grass = 1176 rupees ( given)
\[{\rm{\text{Cost of covering area = Area of square }}} \times {\rm{ \text{Cost of covering one sq meter of area}}}\]
\[\begin{array}{l}
{\rm{1176 = 784}} \times {\rm{C}}\\
{\rm{C = 1176}} \div {\rm{784}}\\
{\rm{C = 1}}{\rm{.5 Rupees}}
\end{array}\]
Here, C is the cost of covering one square meter of area with grass.

Therefore, The rate per sq. meter at which park is covered with grass is 1.5 rupees.

Note:
Solve these types of questions simply by following the two steps.
First find the area of the inner figure formed and then find the cost of covering total or unit as required by the question.