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By selling an article for ₹$48$, a trader loses as much percent as half of the cost price of the article. Calculate the cost price and loss amount of the article.
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Sol. Let the cost price (CP)of the article be $x$
Loss = $\frac{x}{2}\%$ of $x = \frac{x^2}{200}$ (I Mark)
Selling price = $48 = x - \frac{x^2}{200}$ (II Mark)
$\Rightarrow x^2 - 200x + 9600 = 0$ (III Mark)
$\Rightarrow (x - 120)(x - 80) = 0$ (IV Mark)
$\Rightarrow x = 120,80$ (V Mark)
When CP = ₹$120$, Loss = $120 - 48 = 72$ (VI Mark)
When CP = ₹$80$, Loss = $80 - 48 = 32$ (VII Mark)
Loss = $\frac{x}{2}\%$ of $x = \frac{x^2}{200}$ (I Mark)
Selling price = $48 = x - \frac{x^2}{200}$ (II Mark)
$\Rightarrow x^2 - 200x + 9600 = 0$ (III Mark)
$\Rightarrow (x - 120)(x - 80) = 0$ (IV Mark)
$\Rightarrow x = 120,80$ (V Mark)
When CP = ₹$120$, Loss = $120 - 48 = 72$ (VI Mark)
When CP = ₹$80$, Loss = $80 - 48 = 32$ (VII Mark)