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Question
The length and breadth of a rectangular piece of land are in the ratio 5 : 3. If the total cost of fencing it at the rate of ₹24 per meter is ₹9600, find its :
(i) length and breadth
(ii) area
(iii) cost of levelling at the rate of ₹60 per m2.
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Solution
Ratio in length and breadth of a rectangular piece of land = 5 : 3
Cost of fencing = ₹9600
And rate = ₹24 per m
Perimeter =`"Total cost of fencing"/"Rate per m"`
= `9600/24`
= 400 m
Let length = 5x
Then breadth = 3x
∴ Perimeter = 2(l + b)
400 = 2 × (5x + 3x)
∴ 16x = 400
x = `400/16=25`
(i) ∴ Length of land = 5x = 5 × 25 = 125 m
and breadth = 3x = 3 × 25 = 75 m
(ii) Area = l × b
= 125 × 75 = 9375 m2
(iii) Cost of levelling at rate ₹60 per m2
= ₹60 × 9375 m2 = ₹5,62,500
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