A piece of cloth costs Rs.720. If the piece was 5m longer and each metre of cloth costs Rs.2 less; the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per metre?
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let length of cloth piece is x and original rate per metre is y
then,
initially ,
720/x =y -----------(1)
finally ,
720/(x+5)= y-2 ------------(2)
subtract equation (1) -(2)
720/x - 720/(x+5) = y-y+2
720 {1/x - 1/(x+5) }= 2
5 x 360 = x^2 + 5x
x^2 + 5x -1800 = 0
use quadratic formula ,
x ={-5+_root (25+7200)}/2
=(-5+_85)/2 =40, -45
x =40
hence , length of cloth piece is 40 metre
and original rate 18 Rs /metre
then,
initially ,
720/x =y -----------(1)
finally ,
720/(x+5)= y-2 ------------(2)
subtract equation (1) -(2)
720/x - 720/(x+5) = y-y+2
720 {1/x - 1/(x+5) }= 2
5 x 360 = x^2 + 5x
x^2 + 5x -1800 = 0
use quadratic formula ,
x ={-5+_root (25+7200)}/2
=(-5+_85)/2 =40, -45
x =40
hence , length of cloth piece is 40 metre
and original rate 18 Rs /metre
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