SOLUTION: question-A piece of cloth costs Rs.35.If the length of the piece would have been 4 mtr longer and each metre costs Rs.1 less,the cost would have remained unchanged.How long is the
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Question 560531: question-A piece of cloth costs Rs.35.If the length of the piece would have been 4 mtr longer and each metre costs Rs.1 less,the cost would have remained unchanged.How long is the piece?
You can put this solution on YOUR website! let the length of piece of cloth be x
let the rate per metre be y
xy =35
x=35/y
4 mtr longer
and Re 1 less
(x+4)(y-1)=35
both are equal to 35
equate the two
(x+4)(y-1)=xy
xy-x+4y-4 =xy
xy cancels off
-x+4y = 4
substitute x in the equation
-35/y +4y = 4
multiply equation by y
-35y/y + 4y*y= 4y
-35+4y^2=4y
4y^2-4y-35=0
Find the roots of the equation by quadratic formula
a= 4 , b= -4 , c= -35
b^2-4ac= 16 + 560
b^2-4ac= 576
x1=( 4 + 24 )/ 8
x1= 3.5
x2=( 4 -24 ) / 8
x2= -2.5
Ignore negative value
Rate per metre = Rs. 3.50
Price of cloth is Rs.35
35/3.5 = 10 metres
Length of cloth = 10 metres
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