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Profit and Loss: Apples and Oranges

XAT 2016 · Quantitative Ability & Data Interpretation · Hard · Quantitative Ability

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Rani bought more apples than oranges. She sells apples at Rs. 23 apiece and makes 15% profit. She sells oranges at Rs. 10 a piece and makes 25% profit. If she gets Rs. 653 after selling all the apples and oranges, find her profit percentage.

  1. A.

    16.8%

  2. B.

    17.4%

  3. C.

    17.9%

  4. D.

    18.5%

  5. E.

    19.1%

Answer

B

Explanation

Selling price equation: 23x+10y=65323x + 10y = 653, with x>yx > y (integers). Since 10y10y ends in 0, 23x23x must end in 3. So xx ends in 1. Testing x=21x = 21: 23(21)=483  ⟹  10y=170  ⟹  y=1723(21) = 483 \implies 10y = 170 \implies y = 17. (Satisfies x>yx > y). CP of 1 apple = 23/1.15=2023 / 1.15 = 20. CP of 1 orange = 10/1.25=810 / 1.25 = 8. Total CP = 21(20)+17(8)=420+136=55621(20) + 17(8) = 420 + 136 = 556. Total SP = 653. Profit = 653−556=97653 - 556 = 97. Profit percentage = (97/556)×100≈17.4%(97 / 556) \times 100 \approx 17.4\%.

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