Question: Two varieties of sugar are mixed together in a certain ratio. The cost of the mixture per Kg is 0.50 less than that of the superior and 0.75 more than the inferior variety. The ratio in which the superior and inferior varieties of sugar have been mixed is:
A)3:2
B)5:2
C)5:1
D)1:1
E)none of these
“Two Varieties of Sugar are Mixed together in a Certain Ratio GMAT Problem Solving”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
Explanation: the given case identifies the mixture of two different varieties of sugar, inferior and superior variety of sugar, mixed in a certain ratio. The cost of the mixture per kg has been depicted being 0.50 less than superior quality but 0.75 more than inferior variety. In order to find the ratio of the mixture of the varieties of sugar, the problem needs to be solved in the following way-
Let x be the cost of the mixture, the superior variety be S and the Inferior variety by I. accordingly, to find the ratio of the varieties of the sugar in the mixture, it can be implied as-
= (x + 0.5)S + (x-0.75)I = x(S+I)
= Sx + 0.5S + Ix-0.75I =Sx+Ix
= 0.5S=0.75I
\(=\frac{S}{I}=\frac{0.75}{0.5} \Rightarrow \frac{1.5}{1} \Rightarrow \frac{3}{2}\)
Hence, based on the above equation, it can be evaluated that the ratio in which the superior and inferior variety of sugar is mixed together, is 3:2. Therefore, A is the correct answer.
Correct Answer: A
Approach Solution 2:
Explanation: For the given case where two varieties of sugar are mixed in a certain ratio that includes both superior and inferior varieties of sugar. It is given that the cost of the mixture is mainly 0.50 less than the superior quality and 0.75 more than the inferior variety.
Accordingly, in order to find the ratio in which the mixture of two varieties of sugar is present, the following equation is to be solved. Here x is considered as the cost of the superior variety of sugar.
Further, it can be implicated that-
Superior sugar cost = x
inferior sugar cost = x-(.50+.75) => x-1.25
ratio between two sugars in mix = x/(x-1.25)
Hence, the ratio of the sugar mixture can be found from solving the equation equals to-
=> x/(x-1.25)=3/2=3.75/2.50
=> 3/2
Thus, the correct answer for the ratio of the mixture of two different varieties of sugar is 3:2 and hence, A is the correct option.
Correct Answer: A
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