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The question is from CAT Ratio, Mixtures and Averages. Given the details about two alloys, we need to determine the possible values the weight of an ally can take. CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019.

Question 16: 100 kgs of an alloy of tin and lead in the ratio 1:3 is mixed with x kgs of an alloy of tin and lead in the ratio 3:2. If the overall alloy should contain between 40% and 50% tin, what is the range of values x can take?

  1. 100 kgs ≤ x ≤ 200 kgs
  2. 80 kgs ≤ x ≤ 240 kgs
  3. 110 kgs ≤ x ≤ 220 kgs
  4. 75 kgs ≤ x ≤ 250 kgs

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Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: When we add one of the two components of an alloy to another alloy, how does the mixture change.
Alloy 1 Tin 25 Lead 75 Total 100 kg
Alloy 2 Tin
3x / 5
Lead
2x / 5
x kg

The table shows the composition of the two alloys. The total percentage of tin is the total weight of the tin as a percentage of the total weight of the two alloys put together.
Percentage of Tin overall = (25 + \\frac{3x}{5}\\) ) * ( \\frac{100}{100+x}\\) )
This number should be between 40% and 50%
40 ≤ (25 + \\frac{3x}{5}\\) ) * ( \\frac{100}{100+x}\\) ) ≤ 50
Solving the inequality, x has to lie between 75 and 250 kg
Alternatively, we can find the range by thinking of it as two mixtures problems for the two boundary conditions.

(i) 100 kgs of 25% Tin mixed with x kgs of 60% Tin to give 40% Tin → This gives x = 75 kgs.
(ii) 100 kgs of 25% Tin mixed with x kgs of 60% Tin to give 50% Tin → This gives x = 250 kgs.

The question is "what is the range of values x can take?"

Hence, the answer is "75 kgs ≤ x ≤ 250 kgs".

Choice D is the correct answer.

 


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