A mixture containing 50% wine is mixed with another mixture containing 60% wine in the ratio x : y. If the quantity of wine in the final mixture is 51.25%, find the value of x : y.

Here are some tips for solving quantitative aptitude mixture and alligation questions: Alligation is method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: Alligation medial: Used to find the quantity of a mixture given the quantities of its ingredients Alligation alternate: Used to find the amount of each ingredient needed to make a mixture of a given quantity If both the antecedent and the consequent are multiplied or divided by the same number (except 0) then the ratio will remain the same. The rule of allegation formula is:... Show more

Here are some tips for solving quantitative aptitude mixture and alligation questions:

Alligation is method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation:
Alligation medial: Used to find the quantity of a mixture given the quantities of its ingredients
Alligation alternate: Used to find the amount of each ingredient needed to make a mixture of a given quantity

If both the antecedent and the consequent are multiplied or divided by the same number (except 0) then the ratio will remain the same.

The rule of allegation formula is: Quantity of cheaper/ Quantity of dearer = CP of Dearer – Mean Price / Mean Price – CP of cheaper.
You can also write: (Quantity of the Cheaper Substance) : (Quantity of the Dearer Substance) = (d – m) : (m – c). 

The method of the repeated dilutions is another way of achieving the results that are given by the rule of alligation.
Suppose a container contains 'x' units of liquid from which 'y' units are taken out and replaced by water. After n operations, the quantity of pure liquid = [x{1 – (y/n)}n] units. 

You can solve alligation problems using a graphical approach, which looks like a cross.

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