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

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

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New post 25 Mar 2019, 09:30
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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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Solution A is made up of alcohol and water mixed in the ratio of 21:4  [#permalink]

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New post 25 Mar 2019, 15:21
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kiran120680 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


units alcohol combined=5(21/25)+6(2/5)=33/5
units water combined=5(4/25)+6(3/5)=22/5
total A+B volume combined=33/5+22/5=55/5
resultant percent alcohol=(33/5)/(55/5)=.6=60%
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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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New post 28 Mar 2019, 12:53
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Solution A: 21/(21+4) alcohol
Solution B: 2/(2+3) alcohol
5/11 of A + 6/11 of B = 5/11 * 21/25 + 6/11 * 2/5 = 33/55 = 3/5 or 60% alcohol
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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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New post 31 Mar 2019, 11:52
kiran120680 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



The ratio for solution A is alcohol : water = 21x : 4x. Therefore, the volume of solution A is 25x.

The ratio for solution B is alcohol : water = 2y : 3y. Therefore, the volume of solution B is 5y.

When the two solutions are mixed in a ratio of 5 to 6 by volume, we can let x = 1 and y = 6 (notice that the volume of solution A is 25 and that of solution B is 30 and 25:30 = 5:6).

We see that the volume of the mixture is 25 + 30 = 55, of which 21(1) + 2(6) = 33 is alcohol. Therefore, alcohol is 33/55 = 3/5 = 60% of the mixture.

Answer: C
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Re: Solution A is made up of alcohol and water mixed in the ratio of 21:4   [#permalink] 31 Mar 2019, 11:52
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Solution A is made up of alcohol and water mixed in the ratio of 21:4

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