Question

A piece of cloth costs rs 200 .if the piece were 5m longer, and each metre of cloth costed rs 2 less the cost of the piece would have remained unchanged. how long is the piece and what is its original rate per metre.

Answer 1

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

∴, xy=200 -------------(1) and

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

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

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

or, 5y-2x-10=0

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

Putting in (1),

20y=200

or, y=10

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

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Answer 2

Please see the attachment