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Solution A is made up of alcohol and water mixed in the ratio of 21:4

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ganand
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Solution A is made up of alcohol and water mixed in the ratio of 21:4 [#permalink] New post   26 Jul 2017, 05:19
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Solution A is made up of alcohol and water mixed in the ratio of 21:4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2:3 by volume. If Solution A and Solution B are mixed in the ratio of 5:6 by volume, what percent of the resultant mixture is alcohol?

(A) 32.5%
(B) 40%
(C) 60%
(D) 65%
(E) Cannot be determined



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Re: Solution A is made up of alcohol and water mixed in the ratio of 21:4 [#permalink] New post   26 Jul 2017, 05:42
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Assume that both
Solution A & Solution B have 100 units

Since the ratio in solution A is 21:4, there will be 84 units of Alcohol, to 16 units of Water.
Similarly, solution B will have ratio 2:3(40 units Alcohol:60 units water)

Since the solutions are to mixed in the ratio 5:6(we are adding 500 units of Solution A and 600 units of Solution B)

Total concentration of Alcohol : \(\frac{84*5 + 40*6}{100*5 + 100*6} = \frac{420+240}{1100} = \frac{660}{1100} = 60%\)(Option C)
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Re: Solution A is made up of alcohol and water mixed in the ratio of 21:4 [#permalink] New post   26 Jul 2017, 07:15
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Ans :C
Alcohol in Soln A =21/25
Alcohol in Soln B =2/5
Mixed in ratio of 5/11 and 6/11 respectively
=(21/25)*(5/11)+(2/5)*(6/11)
=3/5=60%

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Re: Solution A is made up of alcohol and water mixed in the ratio of 21:4 [#permalink] New post   26 Jul 2017, 08:26
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ganand wrote:
Solution A is made up of alcohol and water mixed in the ratio of 21:4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2:3 by volume. If Solution A and Solution B are mixed in the ratio of 5:6 by volume, what percent of the resultant mixture is alcohol?

(A) 32.5%
(B) 40%
(C) 60%
(D) 65%
(E) Cannot be determined


Solution



    • Since the question asks us to find the percent of alcohol in the mixture. It would be best if we convert everything in percentage and then solve it quickly.
    • If we take Alcohol, then
      o Percentage of Alcohol in Solution A \(= 21*\frac{100}{25} = 84\)%

      o Percentage of Alcohol in Solution B \(= 2*\frac{100}{5} = 40\)%

    • Since the ratio of Solution A: Solution B \(= 5: 6\)
    • The Percentage of Alcohol in the mixture \(= \frac{(5 * 84 + 6 * 40)}{(5+6)}\)
      \(= \frac{660}{11}\)%
      \(= 60\)%

Thus, the correct answer is Option C.

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Re: Solution A is made up of alcohol and water mixed in the ratio of 21:4 [#permalink] New post   01 Aug 2021, 00:53
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Re: Solution A is made up of alcohol and water mixed in the ratio of 21:4 [#permalink]
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