MathematicsOne 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.

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.


  1. A
    1.5 Rs
  2. B
    2 Rs
  3. C
    2.5 Rs
  4. D
    2.75 Rs 

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    Solution:

    Concept: A square will be formed by the path's inner edge. By calculating the area of the inner square, one can determine the area of the remaining portion.
    By deducting twice the path's width from the side of the outer square, one may find the side of the inner square.
    Total cost = Total area × rates per unit
    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
    S = Length of outer square – 2 × Width of path
    Explaining the relationship between the square's area and sides.
    Area of the square = side× side
    Here, A is the area of the inner square.
    Indicate the relationship between the cost of installing grass in the park and its size.
    1176 rupees will be needed to grass the area ( given)
    Cost of covering area = Area of square × Cost of covering one sq. meter of area
    Hence, the correct answer is option 1.
     
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