Multiple choice

Two vessels A and B contain spirit and water mixed in the ratios 3 : 4 and 8 : 5, respectively. Find the ratio in which these mixture should be mixed to obtain a new mixture in vessel containing spirit and water in the ratio 6 : 7.

  1. 5 : 14

  2. 3 : 14

  3. 14 : 3

  4. 6 : 5

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the allegation method: Vessel A (3/7 spirit), Vessel B (8/13 spirit), Target (6/13 spirit). The ratio is (8/13 - 6/13) : (6/13 - 3/7) = (2/13) : (3/91) = 14:3.

AI explanation

Using the alligation method on the fraction of spirit in each mixture, vessel A has 3/7 spirit and vessel B has 8/13 spirit, while the target mixture has 6/13 spirit. The ratio of A to B is the difference between the target and B placed over the difference between A and the target: (8/13 - 6/13) divided by (6/13 - 3/7). This simplifies to (2/13) divided by (3/91), which equals 14/3. The mixtures should be combined in a 14 to 3 ratio.

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