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The Dimensions of a Rectangular Field Are 50 M and 40 M. a Flower Bed is Prepared Inside this Field Leaving a Gravel Path of Uniform Width All Around the Flower Bed. the Total Cost of Laying the - ICSE Class 10 - Mathematics

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Question

The dimensions of a rectangular field are 50 m and 40 m. A flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and gravelling the path at Rs 30 and Rs 20 per square metre, respectively, is Rs 52,000. Find the width of the gravel path.

Solution

Let the width of the gravel path be w m.
Length of the rectangular field = 50 m
Breadth of the rectangular field = 40 m
Let the length and breadth of the flower bed be x m and y m respectively.
Therefore, we have:
x + 2w = 50 … (1)
y + 2w = 40 … (2)
Also, area of rectangular field = 50 m 40 m = 2000 m2
Area of the flower bed = xy m2
Area of gravel path = Area of rectangular field – Area of flower bed = (2000 – xy) m2
Cost of laying flower bed + Gravel path = Area x cost of laying per sq. m
52000 = 30 xy + 20 (2000 – xy)
52000 = 10xy + 40000
xy = 1200
Using (1) and (2), we have:
(50 – 2w) (40 – 2w) = 1200
2000 – 180w + 4w2 = 1200
4w2 – 180w + 800 = 0
w2 – 45w + 200 = 0
w2 – 5w – 40w + 200 = 0
w(w – 5) – 40(w – 5) = 0
(w – 5) (w – 40) = 0
w = 5, 40
If w = 40, then x = 50 – 2w = -30, which is not possible.
Thus, the width of the gravel path is 5 m.

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 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6B | Q: 9
Solution The Dimensions of a Rectangular Field Are 50 M and 40 M. a Flower Bed is Prepared Inside this Field Leaving a Gravel Path of Uniform Width All Around the Flower Bed. the Total Cost of Laying the Concept: Quadratic Equations.
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