Question

a piece of cloth cost rupees 800 if the piece was 5 M long and the rate of cost of cloth per metre was rupees Atlas the cost of the peace would have remained on just how long is the peace and what is the rate of cost per metre​

Answer 1

Answer:

Solution:

Given,

A piece of cloth costs Rs 800.

Let the length of the cloth be x m and the rate of cost per meter be Rs y /m.

So, the cost of cloth = xy

or,800=xy

or,x=800y - (i)

According to the question,

If the price was 5 m longer and the rate of cost of cloth per meter was Rs 8 less, the cost of the piece would have remained unchanged.

or,(x+5)×(y−8)=800

Put value of x from equation (i)

or,(800y+5)(y−8)=800

or,800+5yy×(y−8)=800

or,(800+5y)(y−8)=800y

or,800(y−8)+5y(y−8)=800y

or,800y−6400+5y²−40y=800y

or,5y²+800y−40y−6400−800y=0

or,5y²+760−800y−6400=0

or,5y²−40y−6400=0

or,5(y²−8y−1280)=0

or,y²−8y−1280=0

or,y²−(40−32)y−1280=0

or,y²−40y+32y−1280=0

or,y(y−40)+32(y−40)=0

or,(y+32)(y−40)=0

Either,

y+32=0

∴y=−32

Or,

y−40=0

∴y=40

The rate of cost per meter can not be negative number. So, y = 40.

Put value of y in equation (i), we get,

or,x=80040

∴x=20

So, (x,y) = (20,40)

Therefore, the required length of the piece of cloth is 20m and the rate of cost per meter is Rs 40/m.

Answer 2

Step-by-step explanation:

A piece of cloth cost rupees =800

let A piece of cloth be x m and the cost of cloth rupees be Rs. y per/m

then,

A. T. Q.

xy =Rs800

y=Rs(800/x) ........1

Now

(x+5)(y-8) = 800

or, y - 8 =800/(x+5)

or, (800/x) - 800/(x+5) =8

or, 800[(1/x) - 1/(x+5)] =8

or, 800/8[(x+5-x)/x(x+5)] =1

or, 100[5/(x^2+5x)] =1

or, 500 = x^2+5x

or, x^2+5x - 500 =0

or, x^2+25x -20x -500 =0

or, x(x+25) - 20(x+25)=0

so,( x-20) (x+25)=0

when ( x-20)= 0

x = 20m

when

(x+25)=0

x = -25m which is not exist

the value of x put in equation (1) we get,

20y = 800

y =800/20

y = Rs 40

so, cloth = 20m and rate =Rs 40