Question

A piece of cloth costs Rs. $200$. If the piece was $5m$ longer and each meter of cloth costs Rs. $2$ less the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per meter?

Answer 1

Let the length of the piece be $x$ metres. Then, rate per metre $=Rs.\frac{200}{x}$
New length $=(x+5)$ metres
Since the cost remains same
New rate per metre $=Rs.\frac{200}{x+5}$
It is given that

$\frac{200}{x}-\frac{200}{x+5}=2$

$\Rightarrow \frac{200(x+5)-200x}{x(x+5)}=2\Rightarrow \frac{1000}{x(x+5)}=2$

$\Rightarrow x^2+5x=500\Rightarrow x^2+5x-500=0$$

$\Rightarrow x^2+25x-20x-500=0$

$\Rightarrow (x+25)(x-20)=0\Rightarrow x+25=0$

$orx-20=0\Rightarrow x=20orx=-25$

But $x$ cannot be negative. So, $x=20$

Rate per metre $Rs.\frac{200}{x}=Rs\frac{200}{20}=Rs.10$

Hence the length of the piece of cloth is $20$ meters and rate =Rs. $10$ per meter