# A piece of cloth

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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