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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 $10\ m$.