Let the ratio of the length to the breadth of a flag be 3:2. Let the cost of the cloth required to make the flag be Rs. 4 per square metre and the cost of stitching along its perimeter be Rs. 2 per metre. If the cost of making (the cost of cloth and the cost of stitching) 6 such flags is Rs. 24, then answer the following questions.
How much length (in metre) has to be stitched along the perimeter to make 6 flags in total ?
Answers
Given : ratio of the length to the breadth of a flag be 3:2
Cost of the cloth required to make the flag be Rs. 4 per square metre
cost of stitching along its perimeter be Rs. 2 per metre.
cost of making (the cost of cloth and the cost of stitching) 6 such flags is Rs. 24
To Find : How much length (in metre) has to be stitched along the perimeter to make 6 flags in total ?
Solution:
Length = 3X m
Breadth = 2X m
Perimeter = 2(3X + 2X) = 10X m
Perimeter of 6 Flags = 6 x 10X = 60X m
cost of stitching along its perimeter be Rs. 2 per metre
=> Cost = 2 x 60X = 120X Rs
Area = 3X * 2X = 6X²
Area of 6 Flags = 6 * 6X² = 36 X²
cost of the cloth required to make the flag be Rs. 4 per square metre
Cost = 4 * 36X² = 144X²
144X² + 120X = 24
=> 6X² + 5X = 1
=> 6X² + 5X - 1 = 0
=> 6X² + 6X - X - 1 = 0
=> 6X(X + 1) - (X + 1) = 0
=> (6X - 1)(X + 1) = 0
=> X = 1/6 ,
X = - 1 ( not possible)
Length = 3/6 = 1/2 m
Breadth = 2/6 = 1/3 m
length (in metre) has to be stitched along the perimeter to make 6 flags in total = 60X
= 60(1/6)
= 10 m
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