The ratios of salt and sugar in mixtures A and B are 3 : 4 and 5 : 9,…

2020

The ratios of salt and sugar in mixtures A and B are 3 : 4 and 5 : 9, respectively. A and B are taken in the ratio 2 : 3 and mixed to form a new mixture C. What is the ratio of sugar and salt in C?

  1. A.

    43:27

  2. B.

    25 : 17

  3. C.

    27 : 43

  4. D.

    17 : 25

Attempted by 4 students.

Show answer & explanation

Correct answer: A

CONCEPT

In a mixture-ratio problem, first convert each internal ratio into fractions of the total mixture. When two mixtures are combined in a given quantity ratio, multiply each component fraction by the amount of that mixture before adding the components.

APPLICATION

  1. Let the quantities of mixtures A and B be 2x and 3x.

  2. In A, salt : sugar = 3 : 4, so salt = (3/7) × 2x = 6x/7 and sugar = (4/7) × 2x = 8x/7.

  3. In B, salt : sugar = 5 : 9, so salt = (5/14) × 3x = 15x/14 and sugar = (9/14) × 3x = 27x/14.

  4. Put the totals on denominator 14: total sugar = 16x/14 + 27x/14 = 43x/14; total salt = 12x/14 + 15x/14 = 27x/14.

CROSS-CHECK

Using a concrete scale with A = 28 units and B = 42 units gives sugar = 16 + 27 = 43 and salt = 12 + 15 = 27, so the same ratio appears.

RESULT

Therefore, the ratio of sugar to salt in C is 43 : 27.

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