Question:
The ratio of alcohol to water in two containers, A and B, is 5:3 and 1:3, respectively, with both containers having infinite capacity. Suppose that the aim is to obtain 2.1 litres of liquid, which is composed of equal quantities of alcohol and water. How much liquid should be drawn from A (in litres)?
The ratio of alcohol to water in two containers, A and B, is 5:3 and 1:3, respectively, with both containers having infinite capacity. Suppose that the aim is to obtain 2.1 litres of liquid, which is composed of equal quantities of alcohol and water. How much liquid should be drawn from A (in litres)?
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The Alligation ratio \( (x-m)/(m-y) \) represents the ratio of quantities of the two sources.
Updated On: Jun 12, 2026
- 1.4
- 1.05
- 0.35
- 1.1
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Alligation and mixture ratios.
Step 2: Detailed Explanation:
1. Mixture A has 5/8 alcohol, Mixture B has 1/4 alcohol. Target is 1/2 alcohol.
2. Using alligation: \( |5/8 - 1/2| : |1/4 - 1/2| = 1/8 : 1/4 = 1:2 \).
3. Total parts = 3. Part of A = 1/3 * 2.1 = 0.7.
4. Re-calculating: With 1.4L from A (5/8 alc) and 0.7L from B (1/4 alc): \( 1.4(5/8) + 0.7(1/4) = 0.875 + 0.175 = 1.05 \). Half of 2.1 is 1.05. This balances.
Step 3: Final Answer:
1.4 litres should be drawn from A.
Alligation and mixture ratios.
Step 2: Detailed Explanation:
1. Mixture A has 5/8 alcohol, Mixture B has 1/4 alcohol. Target is 1/2 alcohol.
2. Using alligation: \( |5/8 - 1/2| : |1/4 - 1/2| = 1/8 : 1/4 = 1:2 \).
3. Total parts = 3. Part of A = 1/3 * 2.1 = 0.7.
4. Re-calculating: With 1.4L from A (5/8 alc) and 0.7L from B (1/4 alc): \( 1.4(5/8) + 0.7(1/4) = 0.875 + 0.175 = 1.05 \). Half of 2.1 is 1.05. This balances.
Step 3: Final Answer:
1.4 litres should be drawn from A.
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