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?
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
Let the original length of cloth be $x$ metres.
Original price per metre $= \dfrac{2100}{x}$
After sale, length $= (x + 2)$ metres, new price per metre $= \dfrac{2100}{x+2}$
Given that price reduced by ₹120:
$$\frac{2100}{x} - \frac{2100}{x+2} = 120$$
$$2100\left(\frac{x+2-x}{x(x+2)}\right) = 120$$
$$2100 \times 2 = 120 \cdot x(x+2)$$
$$x^2 + 2x - 35 = 0$$
Factorising:
$$x^2 + 7x - 5x - 35 = 0$$
$$x(x+7) - 5(x+7) = 0$$
$$(x-5)(x+7) = 0$$
$$x = 5 \quad \text{or} \quad x = -7$$
Since length cannot be negative, $x = 5$ m.
Original length = 5 m
Original price per metre $= \dfrac{2100}{5} = $ ₹420
Source: Chapter 4, Quadratic Equations
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Explanation
- Set up one variable for original length; express original price as 2100/x and new price as 2100/(x+2).
- The key condition is the price difference = ₹120 — translate this into the equation and simplify to get a standard quadratic.
- Reject the negative root since length must be positive.
- Examiners award marks for: correct equation formation, correct factorisation, rejecting negative root, and stating both length and price in the conclusion. Missing any step costs marks.