Two containers, A and B, contain mixtures of alcohol and water. Container A has alcohol and water in the ratio 4 : 1, while Container B has them in the ratio 5 : 2. If 10 litres are drawn from Container A and 14 litres from Container B, and the contents are mixed in a third container, what is the ratio of alcohol to water in the new mixture?
3 : 1
Step 1 – Alcohol and water from Container A (10 L, ratio 4:1, total 5 parts):
\(\text{Alcohol}_A = 10 \times \tfrac{4}{5} = 8 \text{ L},\quad \text{Water}_A = 10 \times \tfrac{1}{5} = 2 \text{ L}\)
Step 2 – Alcohol and water from Container B (14 L, ratio 5:2, total 7 parts):
\(\text{Alcohol}_B = 14 \times \tfrac{5}{7} = 10 \text{ L},\quad \text{Water}_B = 14 \times \tfrac{2}{7} = 4 \text{ L}\)
Step 3 – Combine in the new mixture:
\(\text{Total alcohol} = 8 + 10 = 18 \text{ L},\quad \text{Total water} = 2 + 4 = 6 \text{ L}\)
\(\text{Ratio} = 18 : 6 = 3 : 1\)
Hence the answer is option 1.
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