Hi voccubd,

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.

Attachment:

Mixtures 1.png [ 8.12 KiB | Viewed 8789 times ]
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 prices (associated with the word 'per') and the ratio of mixing the two prices are given to us.

Let us keep the price of the second liquid to be 'x$' per liter. The price of the first liquid will be '(x+2)$' per liter. Since the vendor gains 10% on the cost price by selling the mixture at $11, the actual cost price of the mixture needs to be $10. We have also been given the ratio of 3 : 2. Creating the alligation/mixture diagram for the cost prices of the two liquids we get

Attachment:

Mixtures.png [ 6.3 KiB | Viewed 8774 times ]
Subtracting along the diagonals we get

x - 8 = 2

10 - x = 3. Cross multiplying we get

3x - 24 = 20 - 2x -----> 5x = 44 ----->

x = 8.8Since the question asks us the value of x + 2 -------> 8.8 + 2 = 10.8

OA : B

Hope this helps!

CrackVerbal Academics Team

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