Multiple choice

Spirit and Water are mixed in a vessel A in the ratio of 5 : 2 and in the vessel B in the ratio 8 : 5. In what proportion should quantities be taken out from the two vessels so as to form a mixture in which Spirit and Water will be in the ratio of 9 : 4?

  1. 2 : 3

  2. 2 : 7

  3. 7 : 4

  4. 7 : 2
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D Correct answer
Explanation

Using the rule of alligation on the spirit content: Vessel A has 5/7, Vessel B has 8/13, and the target is 9/13. The differences are |8/13 - 9/13| = 1/13 and |5/7 - 9/13| = (65-63)/91 = 2/91. Ratio = (1/13) : (2/91) = 7/91 : 2/91 = 7:2.

AI explanation

By the rule of alligation for mixtures, we find the proportion of spirit to the total mixture in vessel A and vessel B. The fraction of spirit in A is 5/7 and in B is 8/13, while the desired fraction in the final mixture is 9/13. The ratio of quantities from A to B is calculated by the differences between the desired fraction and the individual fractions: (9/13 minus 8/13) to (5/7 minus 9/13), which is 1/13 to 8/91. This simplifies to 7 to 2, meaning the required proportion is 7 : 2.

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