CAT Quantitative Aptitude Questions | CAT Percentage Questions - Mixtures

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The question is from CAT Percentages. This question is a combination of two topics: Percentages and Mixtures. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. Percentages is an important topic for CAT. This question is about mixing two alloys in a ratio to create a new alloy which contains three metals.

Question 3: An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2: 7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?

  1. 30% ≤ x ≤ 40%
  2. 32.5% ≤ x ≤ 42%
  3. 33.33% ≤ x ≤ 40%
  4. 32.25% ≤ x ≤ 40%

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Explanatory Answer

Method of solving this CAT Question from Percentages - Mixtures: What percentage of alloy 1 needs to be mixed with Alloy 2 to get alloy 3.

Alloy 1 Copper Aluminium
2x 3x
Alloy 2 Copper Zinc
2y 7y

If Aluminium and Zinc have to be equal, 3x = 7y. The simplest case occurs at the LCM, when both Aluminium and Zinc are 21kg.

Alloy 1 Copper Aluminium
14 21
Alloy 2 Copper Zinc
6 21

Even a gram of alloy 1 above this level would mean that there is more Aluminium than Zinc in the total alloy. So, this table is a limit on the percentages of different metals.

The percentage of Copper in the total alloy would be (14 + 6)* 100/62 = 32.25%

On the other hand, if we want more Aluminium than Zinc, we can use tons and tons of alloy 1, and only a microgram of Alloy 2. The quantity of alloy 2 can be made so small that its presence can be almost neglected, as it will have as good as zero impact on the overall percentage of copper. This is another extreme case, in which Copper will have 40% weight in the alloy 2?(2+3).

Thus, the percentage of Copper ranges from 32.25% to 40% in this alloy.

The question is "What is the range of values x can take?"
x could range from 32.25% to 40%

Hence, the answer is 32.25% to 40%.

Choice D is the correct answer.


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