A piece of cloth costs Rs. 35.


A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. one less, the cost would remain unchanged. How long is the piece?


Let the length of the piece be x metres.

Then, rate per metre $=\frac{35}{x}$

According to question, new length $=(x+4)$ meters.

Since the cost remain same. Therefore, new rate per metre $=\frac{35}{x+4}$

It is given that


$\frac{35(x+4)-35 x}{x(x+4)}=1$


$x^{2}+4 x=140$

$x^{2}+4 x-140=0$

$x^{2}+14 x-10 x-140=0$




Because $x$ cannot be negative.

Thus, $x=10$ is the require solution.

Therefore, the length of the piece be $x=10$ metres



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