Question

A piece of cloth costs Rs. 200. If the piece was 5 m 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?​

Answer 1

$\huge\underline\mathbb {SOLUTION:-}$

$\mathsf {Let\:the\:length\:of\:piece = x\:m}$

$\mathsf {Rate\:per\:metre = \frac{200}{x}}$

$\mathsf {New\:length = (x + 5)}$

$\mathsf {New\:rate\:per\:metre = \frac{200}{x + 5}}$

$\underline\mathsf \red {ATQ:-}$

$\mathsf {\frac{200}{x} - \frac{200}{x + 5} = 2}$

$\implies \mathsf {\frac{200(x + 5) - 200x}{(x + 5)} = \frac{2}{1} }$

$\implies \mathsf {\frac{200x + 1000 - 200x}{x^2 + 5x} = \frac{2}{1} }$

$\implies \mathsf {x^2 + 5x = 500}$

$\implies \mathsf {x^2 + 5x - 500 = 0}$

$\implies \mathsf {x^2 + 25x - 20x - 500 = 0}$

$\implies \mathsf {x(x + 25) - 20(x + 25) = 0}$

$\implies \mathsf {(x + 25)\:+ (x - 20) = 0}$

$\implies \mathsf {x = -25\:(Neglect) \:or\: x = 20}$

$\mathsf \blue {Rate\:per\:metre = 10}$

Answer 2

Answer:

SOLUTION:−

\mathsf {Let\:the\:length\:of\:piece = x\:m}Letthelengthofpiece=xm

\mathsf {Rate\:per\:metre = \frac{200}{x}}Ratepermetre=

x

200

\mathsf {New\:length = (x + 5)}Newlength=(x+5)

\mathsf {New\:rate\:per\:metre = \frac{200}{x + 5}}Newratepermetre=

x+5

200

\underline\mathsf \red {ATQ:-}

ATQ:−

\mathsf {\frac{200}{x} - \frac{200}{x + 5} = 2}

x

200

−

x+5

200

=2

\implies \mathsf {\frac{200(x + 5) - 200x}{(x + 5)} = \frac{2}{1} }⟹

(x+5)

200(x+5)−200x

=

1

2

\implies \mathsf {\frac{200x + 1000 - 200x}{x^2 + 5x} = \frac{2}{1} }⟹

x

2

+5x

200x+1000−200x

=

1

2

\implies \mathsf {x^2 + 5x = 500}⟹x

2

+5x=500

\implies \mathsf {x^2 + 5x - 500 = 0}⟹x

2

+5x−500=0

\implies \mathsf {x^2 + 25x - 20x - 500 = 0}⟹x

2

+25x−20x−500=0

\implies \mathsf {x(x + 25) - 20(x + 25) = 0}⟹x(x+25)−20(x+25)=0

\implies \mathsf {(x + 25)\:+ (x - 20) = 0}⟹(x+25)+(x−20)=0

\implies \mathsf {x = -25\:(Neglect) \:or\: x = 20}⟹x=−25(Neglect)orx=20

\mathsf \blue {Rate\:per\:metre = 10}Ratepermetre=10

Step-by-step explanation:

hope it will be help you. ......