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

Posted by Chirag Jindal 6 years ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years ago

Let the length of the piece be x metres.
Total cost of the piece =Rs. 35,
Then, rate per metre = Rs. $\frac{35}{x}$
New length = (x + 4) metres
Since the cost remains same.
$\therefore$ New rate per metre = Rs $\frac{35}{x+4}$
According to the question ;
$\frac { 35 } { x } - \frac { 35 } { x + 4 } = 1$
$\Rightarrow \frac { 35 ( x + 4 ) - 35 x } { x ( x + 4 ) } = 1$
$\Rightarrow \frac { 35 x + 140 - 35 x } { x ( x + 4 ) } = 1$
$\Rightarrow$ 140 = x(x + 4)
$\Rightarrow$ 140 = x² + 4x
$\Rightarrow$ $x^2 +4x -140 =0$
$\Rightarrow$ $x^2+14x-10x-140=0$
$\Rightarrow$ x(x + 14) - 10(x + 14) = 0
$\Rightarrow$ (x + 14)(x - 10) = 0
$\Rightarrow$ x - 10 = 0 [ $\because$ Length cannot be negative $\therefore$ x + 14 $\neq$ 0]
$\Rightarrow$ x = 10
Hence, the length of the piece of cloth is 10 m.

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