Multiple choice

A pot contains a mixture of two liquids in the ratio 4 : 5. Another pot contains the same mixture in the ratio 5 : 1. In what ratio should the two mixtures be combined such that the liquids are in the ratio 5 : 4?

  1. 2 : 5

  2. 5 : 2

  3. 1 : 2

  4. 2 : 3

  5. 3 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Use the allegation method. Mixture 1 has 4/9 of liquid A. Mixture 2 has 5/6 of liquid A. Target mixture has 5/9 of liquid A. (5/6 - 5/9) / (5/9 - 4/9) = (15/18 - 10/18) / (1/9) = (5/18) / (2/18) = 5/2.

AI explanation

The proportion of the first liquid in the two pots is 4 divided by 9 and 5 divided by 6 respectively. To obtain a final mixture with the liquids in a 5 to 4 ratio, the required proportion of the first liquid is 5 divided by 9. Applying the rule of alligation, the mixing ratio of the two pots is determined by (5 divided by 6 minus 5 divided by 9) to (5 divided by 9 minus 4 divided by 9), which simplifies to 5 to 2.

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