Multiple choice

Two vessels A and B contain a mixture of milk and water in the ratios 1 : 4 and 5 : 3, respectively. When these mixtures are to be remixed to form a new mixture containing half milk and half water, in what ratio should they be mixed?

  1. 2 : 5

  2. 12 : 5

  3. 5 : 12

  4. 7 : 3

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

Use alligation. Vessel A: 1/5 milk. Vessel B: 5/8 milk. Target: 1/2 milk. |5/8 - 1/2| = 1/8. |1/2 - 1/5| = 3/10. Ratio = (1/8) / (3/10) = 10/24 = 5/12.

AI explanation

Vessel A has a milk concentration of 1 divided by 5, while vessel B has a milk concentration of 5 divided by 8, and the target mixture requires a concentration of 1 divided by 2. Using the rule of alligation, the ratio of their quantities is the difference between vessel B's concentration and the target, divided by the difference between the target and vessel A's concentration. This calculates to (5 divided by 8 minus 1 divided by 2) divided by (1 divided by 2 minus 1 divided by 5), which simplifies to 1 divided by 8 divided by 3 divided by 10. The resulting ratio is 5 to 12.

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