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26 Dec 2016, 21:12
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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48% (02:41) correct
52%
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wrong
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Two liquids are mixed in the ratio 3:2 and the vendor gains 10% by selling the mixture at $11/liter. If the first liquid costs $2 more than the second, find the cost price of first liquid.
A. $8
B. $10.8
C. $6
D. $8.8
E. $4
Is there any way to do this in weighted average method?
A. $8
B. $10.8
C. $6
D. $8.8
E. $4
Is there any way to do this in weighted average method?
11 Jan 2017, 11:32
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C(1.10)=S ===> \(C=11/1.10=10\). The cost price of the mixture is 10$
We have 3 units bought at X$, and 2 units bought at (x-2)$, which gives us a mixture of 5units that costs 10$.
\(3(X)+2(X-2)=5(10)\)
x=54/5=10.8
We have 3 units bought at X$, and 2 units bought at (x-2)$, which gives us a mixture of 5units that costs 10$.
\(3(X)+2(X-2)=5(10)\)
x=54/5=10.8
27 Dec 2016, 13:49
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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.
Mixtures 1.png [ 8.12 KiB | Viewed 28017 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
Mixtures.png [ 6.3 KiB | Viewed 27649 times ]
Subtracting along the diagonals we get
x - 8 = 2
10 - x = 3. Cross multiplying we get
3x - 24 = 20 - 2x -----> 5x = 44 -----> x = 8.8
Since the question asks us the value of x + 2 -------> 8.8 + 2 = 10.8
OA : B
Hope this helps!
CrackVerbal Academics Team
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 28017 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 27649 times ]
Subtracting along the diagonals we get
x - 8 = 2
10 - x = 3. Cross multiplying we get
3x - 24 = 20 - 2x -----> 5x = 44 -----> x = 8.8
Since the question asks us the value of x + 2 -------> 8.8 + 2 = 10.8
OA : B
Hope this helps!
CrackVerbal Academics Team
