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

Given:

Cost of a piece of cloth $=Rs. 35$.

If the piece were 4 m longer and each metre costs Rs. 1 less, the cost would remain unchanged.

To do:

We have to find the length of the piece.

Solution:

Let the original length of the piece of cloth be $x\ m$.

This implies,

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

New length of cloth$=x+4\ m$.

Cost of $1\ m$ of new cloth $=Rs. \frac{35}{x}-1=Rs. \frac{35-x}{x}$.

According to the question,

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

$(x+4)(35-x)=35x$  (On cross multiplication)

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

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

Solving for $x$ by factorization method, we get,

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

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

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

$x+14=0$ or $x-10=0$

$x=-14$ or $x=10$

Therefore, the value of $x$ is $10$.    ($x$ cannot be negative)

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