Multiple choice

Two containers A and B contain alcohol and water in the ratio 4 : 3 and 2 : 3, respectively. If mixtures from both the containers are mixed to obtain a new mixture having half alcohol and half water, find the ratio in which these are mixed.

  1. 4 : 3

  2. 5 : 4

  3. 6 : 5

  4. 7 : 5

  5. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using alligation: Container A has 4/7 alcohol, Container B has 2/5 alcohol. Target is 1/2. |2/5 - 1/2| = 1/10. |4/7 - 1/2| = 1/14. Ratio = (1/10) : (1/14) = 14 : 10 = 7 : 5.

AI explanation

By the rule of alligation, we compare the fraction of alcohol in each container to the desired fraction. The fraction of alcohol in container A is 4/7, in container B is 2/5, and the desired fraction in the final mixture is 1/2. The ratio of the quantities of A and B is (1/2 - 2/5) : (4/7 - 1/2), which equals 1/10 : 1/14. Multiplying both sides by 70 yields the ratio 7 : 5.

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