Question

A piece of cloth costs Rs. 35. If the piece were 4 m longer and each metre costs Re. 1 less, the cost would remain unchanged. The length of the piece is --------m.

Answer 1

$\Rightarrow$ Let the length of the piece be $xm$

$\Rightarrow$ Cost price of cloth $=Rs.35$

$\Rightarrow$ Cost price of $1m$ cloth $=Rs.\frac{35}{x}$

According to the question,

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

$\Rightarrow$ $35-x+\frac{140}{x}-4=35$

$\Rightarrow$ $35x-x^2+140-4x=35x$

$\Rightarrow$ $x^2+4x-140=0$

$\Rightarrow$ $x^2+14x-10x-140=0$

$\Rightarrow$ $x(x+14)-10(x+14)=0$

$\Rightarrow$ $(x+14)(x-10)=0$

$\Rightarrow$ $x+14=0$ and $x-10=0$

$\therefore$ $x=-14$ and $x=10$

Length cannot be negative.

$\therefore$ The length of the piece is $10m$.