Question

The total cost of a certain length of a piece of cloth is < 200. If the piece
was 5 m longer and each metre of cloth costs < 2 less, the cost of the piece
would have remained unchanged. How long is the piece and what is its
original rate per metre ?plzz answer fast

Answer 1

let the length of the cloth be x and cost of cloth per m be y then, x * y = 200 so, y = 200/x ....(1) now, If the piece were 5m longer, and each meter of cloth costed Rs 2 less, then, (x+5)(y -2) = 200. xy -2x + 5y -10 = 200 putting the value of (1), we get, 1000/x - 2x = 200 - 190 1000 -2x = 10x 500 -x = 5x x +5x - 500 = 0 x +25x -20x -500 =0 x(x+25) -20(x+25) = 0 (x-20) (x+25) = 0 so, x= 20m (neglecting x= -25) 

Answer 2

let the original rate be Rs. x per metre :
and the piece of cloth be y m long, then;

Cost of piece = 200
xy = 200
x = 200/y

According to the given conditions;
New cost of the piece = (y+5)(x-2)

(y+5)(x-2) = 200
xy-2y+5x-10 = 200
2y-5x+10 = 0

2y -5(200/y) +10 = 0
2y- 1000/y = -10
y - 500/y = -5
y²-500 = -5y
y²-5y-500 = 0

y²+20y-25y-500 = 0
y(y+20) -25(y+20) = 0
(y-25) (y+20) = 0
y = 25 and -20

As the length of a piece of cloth can't be negative hence y=25

x = 200/y
x = 200/25
x = 8
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Hence the piece is 25m long and it's original rate is Rs. 8 per metre