Question

A piece of cloth costs 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

Let original rate of cloth per metre = x Rs

then, length of cloth

when its cost is 200 = 200/x metres

In the given case,

$the \: length \: of \: cloth \: is \: increased \: = \frac{200}{x} + 5$

$rate\: of \: cloth \: per \: metre \: is \: decreased \: = x - 2 \:</em></strong><strong><em>$

It is given that when length of cloth is increased by 5 and rate of cloth per metre is decreased by 2 then the cost of cloth remain unchanged means cost of cloth will be 200 Rs

So,

( length of cloth × rate per metre = cost of cloth)

I. e,

$( \frac{200}{x} + 5)(x - 2) = 200 \\ \\ (\frac{200 + 5x}{x} )(x - 2) = 200 \\ \\ (200 + 5x)(x - 2) = 200x \\ \\ 200x - 400 + 5{x}^{2} - 10x = 200x \\ \\(200x \: being \: on \: both \: sides \: will \: be \: eliminated) \\ 5 {x}^{2} - 10x - 400 = 0 \\ \\ (dividing \: by \: 5 \: both \: sides) \\ {x}^{2} - 2x - 80 = 0 \\ \\ {x}^{2} - 10x + 8x - 80 = 0 \\ \\ x(x - 10) + 8(x - 10) = 0 \\ \\ (x + 8)(x - 10) = 0 \\ \\ x = - 8 \: or \: x = 10$

So from we get two values of x from which one is negative,,

but cost cannot be negative hence, we will take

x = 10

SO,

ORIGINAL RATE PER METRE WILL BE = x = 10 Rs

length of piece of cloth = 200/x = 200/10= 20 m.

Answer 2

Answer:

Let original rate of cloth per metre = x Rs

then, length of cloth

when its cost is 200 = 200/x metres

In the given case,

the \: length \: of \: cloth \: is \: increased \: = \frac{200}{x} + 5thelengthofclothisincreased=

x

200

+5

rate\: of \: cloth \: per \: metre \: is \: decreased \: = x - 2 \:rateofclothpermetreisdecreased=x−2

It is given that when length of cloth is increased by 5 and rate of cloth per metre is decreased by 2 then the cost of cloth remain unchanged means cost of cloth will be 200 Rs

So,

( length of cloth × rate per metre = cost of cloth)

I. e,

\begin{lgathered}( \frac{200}{x} + 5)(x - 2) = 200 \\ \\ (\frac{200 + 5x}{x} )(x - 2) = 200 \\ \\ (200 + 5x)(x - 2) = 200x \\ \\ 200x - 400 + 5{x}^{2} - 10x = 200x \\ \\(200x \: being \: on \: both \: sides \: will \: be \: eliminated) \\ 5 {x}^{2} - 10x - 400 = 0 \\ \\ (dividing \: by \: 5 \: both \: sides) \\ {x}^{2} - 2x - 80 = 0 \\ \\ {x}^{2} - 10x + 8x - 80 = 0 \\ \\ x(x - 10) + 8(x - 10) = 0 \\ \\ (x + 8)(x - 10) = 0 \\ \\ x = - 8 \: or \: x = 10\end{lgathered}

(

x

200

+5)(x−2)=200

(

x

200+5x

)(x−2)=200

(200+5x)(x−2)=200x

200x−400+5x

2

−10x=200x

(200xbeingonbothsideswillbeeliminated)

5x

2

−10x−400=0

(dividingby5bothsides)

x

2

−2x−80=0

x

2

−10x+8x−80=0

x(x−10)+8(x−10)=0

(x+8)(x−10)=0

x=−8orx=10

So from we get two values of x from which one is negative,,

but cost cannot be negative hence, we will take

x = 10

SO,

ORIGINAL RATE PER METRE WILL BE = x = 10 Rs

length of piece of cloth = 200/x = 200/10= 20 m.

hope it will help you

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