Before I jump in to solve this question, let me provide you a brief explanation of how to approach weighted average questions on the GMAT. Weighted average questions can be easily solved by making use of the alligation/mixture diagram given below.

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Putting in values in the alligation/mixture diagram and subtracting along the diagonals gives us a ratio in which two quantities are mixed. This ratio can now be used to find out what specific amounts of two quantities need to be mixed to obtain a particular mixture.

The only thing that you need to keep in mind here is that the values you need to use, that is the higher value, lower value and mean value have to be values which are associated with the word 'per' (percents, average, per km, per kg etc.).

The alligation/mixture diagram proves useful not only when mixing solutions or combining solids but also to explain the weighted average concept (the word average is also associated with the word per i.e. if the average marks of the class is 80, then it can be understood as 80 marks per student). Say if we have a class A where the average marks is 80 and another class B where the average marks is 70 and the combined average of both class A and B is 74, then we can definitely comment upon which class has the greater number of students. If we represent the average values in the mixture diagram, the ratio of students of Class A and Class B will be 2 : 3. This clearly indicates that class B has the greater number of students.

Now this alligation/mixture diagram can also be used in the above question, since we are mixing two percentages. So creating the alligation/mixture diagram for the percentage of raisins we get

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Now since the ratio of the second mix to the first mix has to be 1 : 4, and since the 2nd mix is 10 pounds raisins we need 40 pounds of the 1st mix. This means we will require an additional

35 pounds of the first mix.

Hope this helps!

CrackVerbal Academics Team

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