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Gopal Fruit Juice Replacement

XAT 2012 · Quantitative Ability & Data Interpretation · Medium · Mixtures and Alligations

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Gopal sells fruit juice mixture using orange juice and pineapple juice. Gopal prepares this mixture by drawing out a jug of orange juice from a 10 litre container filled with orange juice, and replacing it with pineapple juice. If Gopal draws out another jug of the resultant mixture and replaces it with pineapple juice, the container will have equal volumes of orange juice and pineapple juice. The volume of the jug in litres, is

  1. A.

    2

  2. B.

    < 2 and ≤ 2.5

  3. C.

    2.5

  4. D.

    2.5 and ≤ 3

  5. E.

    ≥ 3

Answer

D

Explanation

Let volume of jug be vv. After two replacements, remaining orange juice = 10(1−v10)2=510\left(1 - \frac{v}{10}\right)^2 = 5. (1−v10)2=0.5  ⟹  1−v10=12≈0.707\left(1 - \frac{v}{10}\right)^2 = 0.5 \implies 1 - \frac{v}{10} = \frac{1}{\sqrt{2}} \approx 0.707. v10=0.293  ⟹  v=2.93\frac{v}{10} = 0.293 \implies v = 2.93 litres. Since 2.932.93 lies between 2.52.5 and 33, option D is correct.

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