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The total cost of certain piece of cloth was ₹$2,100$. During special sale time, the shopkeeper offered $2$ m extra cloth for free thus reducing the price of cloth per metre by ₹$120$. What was the original per metre price of cloth and its length ?
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Sol. Let the original length of cloth be $x$ metre.
$\therefore$ Original cost is $\frac{2100}{x}$ per metre.
According to the question,
$\frac{2100}{x} - \frac{2100}{x+2} = 120$ (I) (2 Marks)
$\Rightarrow x^2 + 2x - 35 = 0$ (II) (1 Mark)
$\Rightarrow (x + 7) (x - 5) = 0$ (III) (1 Mark)
$\Rightarrow x = -7,5$
$\therefore x \neq -7$
$\therefore x = 5$ (IV) ($\frac{1}{2}$ Mark)
$\therefore$ The original price of cloth per metre is ₹$420$ and original length is $5$ m. (V) ($\frac{1}{2}$ Mark)
$\therefore$ Original cost is $\frac{2100}{x}$ per metre.
According to the question,
$\frac{2100}{x} - \frac{2100}{x+2} = 120$ (I) (2 Marks)
$\Rightarrow x^2 + 2x - 35 = 0$ (II) (1 Mark)
$\Rightarrow (x + 7) (x - 5) = 0$ (III) (1 Mark)
$\Rightarrow x = -7,5$
$\therefore x \neq -7$
$\therefore x = 5$ (IV) ($\frac{1}{2}$ Mark)
$\therefore$ The original price of cloth per metre is ₹$420$ and original length is $5$ m. (V) ($\frac{1}{2}$ Mark)