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?
- A.
43:27
- B.
25 : 17
- C.
27 : 43
- 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
Let the quantities of mixtures A and B be 2x and 3x.
In A, salt : sugar = 3 : 4, so salt = (3/7) × 2x = 6x/7 and sugar = (4/7) × 2x = 8x/7.
In B, salt : sugar = 5 : 9, so salt = (5/14) × 3x = 15x/14 and sugar = (9/14) × 3x = 27x/14.
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.