Multiple choice

The ratio of white paint and tarpin oil in two different buckets is 2 : 3 and 4 : 5. In what ratio are we required to mix the mixtures of two buckets in order to get a new mixture which has the ratio of tarpin oil and white paint equal to 7 : 5?

  1. 5 : 3

  2. 2 : 3

  3. 3 : 4

  4. 1 : 4

  5. None of these
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A Correct answer
Explanation

Bucket 1: White/Tarpin = 2/3. Bucket 2: White/Tarpin = 4/5. Target: Tarpin/White = 7/5, so White/Tarpin = 5/7. Use allegation on the fraction of white paint: (4/9 - 5/7) / (5/7 - 2/5) = (28-45)/63 / (25-14)/35 = (-17/63) / (11/35) = (-17/63) * (35/11) = -85/99. The ratio is 5:3.

AI explanation

We must use the ratio of white paint to the total mixture for our calculations, which is 2/5 for the first bucket and 4/9 for the second. The desired new mixture must have a tarpin to white ratio of 7 : 5, meaning the white paint to total ratio is 5/12. By the rule of alligation, the required mixing ratio is (5/12 - 4/9) : (2/5 - 5/12), which equals 1/36 : 1/60. Multiplying by the least common multiple of 180 gives the final ratio of 5 : 3.

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