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Repeated replacement of wine

CMAT 2018 · Quantitative Techniques & Data Interpretation · Medium · Mixtures and Alligations

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From a jar of wine containing 32 litres, 4 litres is drawn out, and the jar is filled up with water. If the same proportion of wine is further drawn out two more times, what proportion of wine to water will be there in the resulting mixture?

  1. A.

    245:166

  2. B.

    343:169

  3. C.

    363:173

  4. D.

    323:189

Answer

B

Explanation

Fraction of wine retained in each step = 1−432=781 - \frac{4}{32} = \frac{7}{8}. After 3 operations, wine remaining = 32×(78)3=32×343512=34316=21.437532 \times (\frac{7}{8})^3 = 32 \times \frac{343}{512} = \frac{343}{16} = 21.4375 litres. Water remaining = 32−21.4375=10.562532 - 21.4375 = 10.5625 litres. Ratio of wine to water = 21.437510.5625=343169\frac{21.4375}{10.5625} = \frac{343}{169}.

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