Ratio of volumes of two containers which are filled with mixture of syrup and water is 2: 3 and the ratio of syrup and water in each contains is (5 : 1) and (3 : 1) respectively. If both containers are mixed together what will be the ratio of syrup and water in resultant mixture?
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$45 : 19$
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$12 : 5$
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$47 : 13$
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$9 : 7$
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None of these
C
Correct answer
Explanation
Container 1 has syrup:water in 5:1 ratio with total volume 2x. So syrup = 5/6 × 2x = 5x/3, water = 1/6 × 2x = x/3. Container 2 has syrup:water in 3:1 ratio with total volume 3x. So syrup = 3/4 × 3x = 9x/4, water = 1/4 × 3x = 3x/4. Total syrup = 5x/3 + 9x/4 = (20x+27x)/12 = 47x/12. Total water = x/3 + 3x/4 = (4x+9x)/12 = 13x/12. Ratio of syrup:water = 47x/12 : 13x/12 = 47:13, which is option C.