Question

A piece of cloth costs $\mathrm{Rs}35$. If the piece were $4\mathrm{m}$ longer and each meter costs $\mathrm{Rs}1$ less, the cost would remain unchanged. How long is the piece?

Answer 1

Step 1:

Form a quadratic equation:

Let the length of the piece be $x\mathrm{m}$.

Given that the cost price of cloth is $\mathrm{Rs}35$.

The cost price of one meter cloth is $\mathrm{Rs}\frac{35}{x}$

When the piece was $4\mathrm{m}$ longer, the length will be $\left(x+4\right)\mathrm{m}$

By given condition,

$\begin{array}{rcl}\left(x+4\right)\left(\frac{35}{x}-1\right)& =& 35\\ & \Rightarrow & 35-x+\frac{140}{x}-4=35\\ & \Rightarrow & 35x-x^2+140-4x=35x\\ & \Rightarrow & x^2+4x-140=0\end{array}$

Step 2:

Solve the quadratic equation:

Factorize the given equation and find its roots.

$\begin{array}{rcl}{x}^2+4x-140& =& 0\\ & \Rightarrow & x^2+14x-10x-140=0\\ & \Rightarrow & x\left(x+14\right)-10\left(x+14\right)=0\\ & \Rightarrow & \left(x-10\right)\left(x+14\right)=0\\ & \Rightarrow & x-10=0\mathrm{or}x+14=0\\ & \Rightarrow & x=10\mathrm{or}x=-14\end{array}$

So, the roots are $x=10\mathrm{and}x=-14$.

But length cannot be negative, Rejecting $x=-14$.

So, the required length of piece is $10\mathrm{m}$.

Final answer:

The required length of piece is $10\mathrm{m}$.