Question

An article is marked $x\%$ above the cost price. A discount of $\frac{2}{3}x\%$ is given on the marked price. If the profit is $4\%$ of the cost price and the value of $x$ lies between 25 and 50, then the value of $50\%$ of $x$ is?

Accepted Answer

D. Selling Price $SP = CP \left(1 + \frac{x}{100}ight)\left(1 - \frac{2x}{300}ight) = 1.04 \cdot CP$. $\left(1 + \frac{x}{100}ight)\left(1 - \frac{2x}{300}ight) = 1.04$ $\Rightarrow (100 + x)(300 - 2x) = 1.04 	imes 30000 = 31200$. $30000 + 100x - 2x^2 = 31200 \Rightarrow 2x^2 - 100x + 1200 = 0 \Rightarrow x^2 - 50x + 600 = 0$. Solving gives $x = 30$ or $x = 20$. Since $25 < x < 50$, $x = 30$. Value of $50\%$ of $x = 0.5 	imes 30 = 15$.

Profit, Loss and Discount

Explanation

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