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Profit, Loss and Discount

XAT 2019 · Quantitative Ability & Data Interpretation · Medium · Arithmetic

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An article is marked x%x\% above the cost price. A discount of 23x%\frac{2}{3}x\% is given on the marked price. If the profit is 4%4\% of the cost price and the value of xx lies between 25 and 50, then the value of 50%50\% of xx is?

  1. A.

    12

  2. B.

    16

  3. C.

    13

  4. D.

    15

  5. E.

    20

Answer

D

Explanation

Selling Price SP=CP(1+x100)(1−2x300)=1.04⋅CPSP = CP \left(1 + \frac{x}{100}\right)\left(1 - \frac{2x}{300}\right) = 1.04 \cdot CP. (1+x100)(1−2x300)=1.04\left(1 + \frac{x}{100}\right)\left(1 - \frac{2x}{300}\right) = 1.04 ⇒(100+x)(300−2x)=1.04×30000=31200\Rightarrow (100 + x)(300 - 2x) = 1.04 \times 30000 = 31200. 30000+100x−2x2=31200⇒2x2−100x+1200=0⇒x2−50x+600=030000 + 100x - 2x^2 = 31200 \Rightarrow 2x^2 - 100x + 1200 = 0 \Rightarrow x^2 - 50x + 600 = 0. Solving gives x=30x = 30 or x=20x = 20. Since 25<x<5025 < x < 50, x=30x = 30. Value of 50%50\% of x=0.5×30=15x = 0.5 \times 30 = 15.

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