Question

A Piece of cloth costs ₹ 200. If the piece was 5m 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 the original rate per metre?

Answer 1

Let the length of the piece be x m.
Rate per metre = ₹ 200/x

New length = x +5 m
New rate per metre = ₹ 200/x+5

ATQ
200/x - 200/x+5 = 2
200(x+5) - 200x / x(x+5) = 2
200x + 1000 -200x / x² +5x = 2
1000 / x² +5x = 2
2(x² +5x ) = 1000
x² + 5x = 1000/2
x² + 5x = 500
x² +5x -500= 0
x² +25x -20x -500= 0
x(x+25) -20(x +25)= 0
(x-20) ( x+25)= 0

(x-20) = 0 or  ( x+25)= 0

x = 20  or  x = -25 (Length can't be negative)
So,x = 20.

Rate per metre = ₹ 200/x = ₹ 200/20= ₹ 10.

Hence, the length of the piece of cloth is 20 m and the rate = ₹ 10 per m.

HOPE THIS WILL HELP YOU..

Answer 2

Hey There! ☺

Nice Questions! ♥

Let's unlock the answers now…

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Important so read it:-

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Let the piece of cloth is x metre and it costs Rs.y/metre. Then by the given conditions 

∴, xy=200 -------------(1) and

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(x+5)(y-2)=200

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or, xy+5y-2x-10=200

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or, 200+5y-2x-10=200

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or, 5y-2x-10=0

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or, 5y=2x+10

or, y=(2x+10)/5

Putting in (1),

x(2x+10)/5=200

or, x(2x+10)=200×5

or, 2x²+10x=1000

or, x²+5x-500=0

or, x²+25x-20x-500=0

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

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

either, x+25=0

or, x=-25

or, x-20=0

or, x=20

Since the length of the cloth can not be negative,

∴, x=20 metre

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Putting in (1),

20y=200

or, y=10

∴, the cloth is 20 m long and the original rate is Rs. 10/metre:)

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Hope my answer helped … ☺