Question

A piece of cloth costs INR 35. If the piece were 4m longer and each metre costs INR 1 less, the cost would remain unchanged. How long is the piece?

Answer 1

Let the length of cloth be x

Therefore xost of $1m$ cloth $=\frac{35}{x}$

Now $\frac{35}{x}–1=\frac{35}{x+4}$

$⟹$ $\frac{35}{x}–1=\frac{35}{x+4}$

$⟹$ $\frac{35–x}{x}=\frac{35}{x+4}$

$⟹35(x+4)–x^2–4x=35x$
$⟹140–x^2–4x=0$

$⟹x^2+4x-140=0$

$⟹(x-10)(x+14)=0$

$⟹x=10,x\ne -14$

Therefore, Length of piece $=10m$