Combining Two Milk and Water Mixtures

CAT 2017 Slot 2 · QA · Medium · Mixtures

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Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?

  1. A.

    27:14

  2. B.

    27:13

  3. C.

    27:16

  4. D.

    27:18

Answer

B

Explanation

Fraction of milk in Bottle 1 = 79\frac{7}{9}

Fraction of milk in Bottle 2 = 913\frac{9}{13}

Target fraction of milk = 34\frac{3}{4}

Using alligation on milk fraction: Ratio=34−91379−34=39−365228−2736=352136=3×3652=2713\text{Ratio} = \frac{\frac{3}{4} - \frac{9}{13}}{\frac{7}{9} - \frac{3}{4}} = \frac{\frac{39 - 36}{52}}{\frac{28 - 27}{36}} = \frac{\frac{3}{52}}{\frac{1}{36}} = \frac{3 \times 36}{52} = \frac{27}{13}

Thus, the required ratio is 27 : 13.

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