CAT 2018 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Mixtures Questions | Question 11

In CAT 2018 Question Paper, we witnessed a bunch of beautiful questions that give utmost importance to the basics and fundamentals of concepts. This question from Mixtures is one such question where in you need to compute the unknown concentration of a solution. If you feel your fundas a bit shaky, CAT previous year paper questions can be your holy grail. They will aid you in grasping the basic concepts and help you solve problems in a well-structured manner.
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Question 11 : A 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1:3 by volume. This mixture is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution, then the unknown concentration of S is

  1. 50%
  2. 55%
  3. 48%
  4. 52%

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Explanatory Answer

Method of solving this CAT Question from Mixtures

Given that 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1:3 by volume
CAT 2018 Question Paper Quants Slot 2 Mixtures

This M is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution ,then the unknown concentration of S has to be found
CAT 2018 Question Paper Quants Slot 2 Mixtures

Equal quantities of mixture and 20% ethanol solution are mixed in equal ratio to get 31.25%
The mixture and 20% ethanol solution are mixed in equal ratio to get 31.25%. This 31.25% is 11.25% more than this 20%. This mixture must be 11.25% more than 31.25% so mixture is equal to 42.5%
CAT 2018 Question Paper Quants Slot 2 Mixtures

This mixture 42.5% is mixed in the ratio 1:3
CAT 2018 Question Paper Quants Slot 2 Mixtures

Using allegations we can find this 22.5% which should be in the ratio 1:3 so the other one is 7.5%
S = 42.5 + 7.5
S = 50%
Here to find the solution, do the second thing first and then go to the first thing
The second one is mixed in the ratio 1 : 1 so that the final thing should be bang in the middle

The question is "A 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1:3 by volume. This mixture is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution, then the unknown concentration of S is"

Hence, the answer is 50%

Choice A is the correct answer.

 

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