SOLUTION: the dimension of a rectangular field are 50 m by 40 m. A flower bed is prepared inside this field leaving a graval path of uniform all around the flower bed. The total cost of layi

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Question 884265: the dimension of a rectangular field are 50 m by 40 m. A flower bed is prepared inside this field leaving a graval path of uniform all around the flower bed. The total cost of laying the flower bed and gravelling the path at rupees 30 and rupees 20 per square meter respectively is rupees 52000. find the widht of gravel path
Answer by geetha_rama(94) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the width of gravel path.
Area of flower bed = (50-x)*(40-x) = x ^2 - 90x + 2000
Area of gravel path = total area - area of flowerbed
= 2000 - (x^2 -90x + 2000) = 90x -x^2
Cost of laying flower bed and gravel path is 52000
Flower bed cost = (x^2 - 90x + 2000)×30
Gravel path cost =( 90x - x^2)*20
(x^2-90x+2000)×30+(90x-x^2)×20=52000
x^2 (30-20)-90x (30-20)+60000=52000
10x^2-900x+8000=0
x^2-90x+800=0
x^2-10x-80x+800=0
x=10, 80
Width of the gravel path is 10m