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CAT Previous Year Paper | CAT Mixtures Questions | Question 11

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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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