Q. 314.4( 7 Votes )

A piece of cloth

Answer :

Let the piece of cloth is x metre and it costs Rs. y/metre.

Then by the given conditions


As, the total cost of cloth = 200


xy = 200 ...... (i)


Also, given if length will increase by 5 m cost will decrease by Rs 2.


(x + 5)(y – 2) = 200


xy + 5y – 2x – 10 = 200


200 + 5y – 2x – 10 = 200


5y – 2x – 10 = 0


5y = 2x + 10



Putting this in (i),



x(2x + 10) = 200×5


2x2 + 10x = 1000


x2 + 5x – 500 = 0


x2 + 25x – 20x – 500 = 0


x(x + 25) – 20(x + 25) = 0


(x + 25)(x – 20) = 0


So, either x = – 25 or x = 20


As the length of the cloth cannot be negative,


So, x = 20 metre


Putting in (i),


20y = 200


y = 10


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


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