The problem with folks who are getting 5/12 as the answer, the point you folks are messing up is that you are trying to balance the missing components (by adding) to Olive oil. (I will explain this while calculating blotched mix)

I am just using the fractions given in the question, and not taking any LCM as suggested in few posts (to avoid confusion)

Original mix.Olive oil = 5/8

Vinegar = 1/4

Remaining = 1 -(5/8+1/4) = 1/8

Even mixture of salt, pepper and sugar = (1/8)/3 = 1/24 each.

Blotched mix.Olive oil = 5/8

Vinegar = 2 * 1/4 = 1/2

Remaining = 1/24 + 1/24

Folks are working this out as 1 - ( vinegar + remaining) = 1 - (1/2 + 1/24 + 1/24) = 1 - (7/12) = 5/12 (and hence this is understood as the proportion of Olive oil)

The mistake is that, Olive oil's proportion is not changed and is calculated as below.Proportion of olive oil in blotched mix = Olive oil / sum of components in blotched mix.

= (5/8) / ( 5/8 + 1/2 + 1/24 + 1/24)

= (5/8) / ( 15/24 + 12/24 + 1/24 + 1/24)

= (5/8) / ( 29/24)

= 5/8 x 24/29

= 15/29 (ans)

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