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Percentage Changes and Net Effect

XAT 2018 · Quantitative Ability & Data Interpretation · Medium · Quantitative Aptitude

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The price of a product is P. A shopkeeper raises its price by X% and then offers a discount of Y% on the raised price. The discounted price again becomes P. If Y is the difference between X and Y, then find X.

  1. A.

    20

  2. B.

    25

  3. C.

    50

  4. D.

    100

  5. E.

    None of the above

Answer

D

Explanation

Given Y=X−Y  ⟹  X=2YY = X - Y \implies X = 2Y. Net change: (1+X100)(1−Y100)=1  ⟹  (1+2Y100)(1−Y100)=1\left(1 + \frac{X}{100}\right)\left(1 - \frac{Y}{100}\right) = 1 \implies \left(1 + \frac{2Y}{100}\right)\left(1 - \frac{Y}{100}\right) = 1. 1+Y100−2Y210000=1  ⟹  Y100=2Y210000  ⟹  Y=501 + \frac{Y}{100} - \frac{2Y^2}{10000} = 1 \implies \frac{Y}{100} = \frac{2Y^2}{10000} \implies Y = 50. Therefore, X=2Y=100X = 2Y = 100.

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