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The total cost of a certain piece of cloth is ₹200 . If the piece was 5m longer and each metre of cloth costs ₹2 less , the cost of the piece would remain unchanged. How long is the piece and what is its original rate per metre.(4 marks)

Posted by Rani Mishra ??? 5 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Rani Mishra ??? 5 years, 8 months ago

Thanks

Yogita Ingle 5 years, 8 months ago

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.

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