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# PS Mixtures: Ratio of milk and water

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Manager
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Mixtures [#permalink]  16 Aug 2011, 16:16
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Two vessels contain mixtures of milk and water in the ratio of 4:9 in the first vessel and in the ratio of 2:7 in the second vessel. In what ratio should the contents be mixed such that the resultant mixture has milk and water in the ratio of 2:5.
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Re: Mixtures [#permalink]  16 Aug 2011, 22:07
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maheshsrini wrote:
Two vessels contain mixtures of milk and water in the ratio of 4:9 in the first vessel and in the ratio of 2:7 in the second vessel. In what ratio should the contents be mixed such that the resultant mixture has milk and water in the ratio of 2:5.

By just considering milk from the total parts:

I guess it should be the reciprocal of:
\frac{\frac{4}{13}-\frac{2}{7}}{\frac{2}{7}-\frac{2}{9}}
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Re: Mixtures [#permalink]  16 Aug 2011, 23:30
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Let 1st vessel contains X liters of mixture of milk and water.
Milk in 1st vessel = 4/13x
Water in 1st vessel=9/13x
Let 2nd vessel contains Y liters of mixture of milk and water
Milk in 2nd vessel = 2/9y
Water in 2nd vessel =7/9y
Let the two mixture combine such that the milk to water ratio is 2:5
4x/13 + 2y/9 / 9x/13 +7/9y =2/5
36x+26y/81x+91y=2/5
180x+130y=162x+182y
18x=52y
x/y=26/9
Hence mixture from vessel 1 and vessel 2 should be mixed in the ratio 26/9 for milk and water to be in ratio 2:5
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Re: Mixtures [#permalink]  17 Aug 2011, 05:32
Let 1st vessel contains X liters of mixture of milk and water.
Milk in 1st vessel = 4/13x
Water in 1st vessel=9/13x
Let 2nd vessel contains Y liters of mixture of milk and water
Milk in 2nd vessel = 2/9y
Water in 2nd vessel =7/9y
Let the two mixture combine such that the milk to water ratio is 2:5
4x/13 + 2y/9 / 9x/13 +7/9y =2/5
36x+26y/81x+91y=2/5
180x+130y=162x+182y
18x=52y
x/y=26/9
Hence mixture from vessel 1 and vessel 2 should be mixed in the ratio 26/9 for milk and water to be in ratio 2:5

well..i get ur method..but a quick stupid ques...y didn't u take Milk as x & Water as y in both the vessels..
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Re: Mixtures [#permalink]  18 Aug 2011, 02:05
Expert's post
DeeptiM wrote:
Let 1st vessel contains X liters of mixture of milk and water.
Milk in 1st vessel = 4/13x
Water in 1st vessel=9/13x
Let 2nd vessel contains Y liters of mixture of milk and water
Milk in 2nd vessel = 2/9y
Water in 2nd vessel =7/9y
Let the two mixture combine such that the milk to water ratio is 2:5
4x/13 + 2y/9 / 9x/13 +7/9y =2/5
36x+26y/81x+91y=2/5
180x+130y=162x+182y
18x=52y
x/y=26/9
Hence mixture from vessel 1 and vessel 2 should be mixed in the ratio 26/9 for milk and water to be in ratio 2:5

well..i get ur method..but a quick stupid ques...y didn't u take Milk as x & Water as y in both the vessels..

Because the volume of milk and water in the two vessels is not the same. The volume of the mixture in the two vessels is not the same too. If you are getting confused with variables, try fluke's method. It is quick and clean.

I have discussed a similar question here: http://www.veritasprep.com/blog/2011/04 ... -mixtures/
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Manager
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PS Mixtures: Ratio of milk and water [#permalink]  08 Oct 2011, 16:41
Two vessels contain mixtures of milk and water in the ration of 4:9 in the 1st vessel and 2:7 in the 2nd vessel. In what ratio should the contents of these two vessels be mixed such that the resultant mixture has milk and water in the ratio of 2:5?
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Re: PS Mixtures: Ratio of milk and water [#permalink]  09 Oct 2011, 02:09
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Re: PS Mixtures: Ratio of milk and water [#permalink]  09 Oct 2011, 02:26
maheshsrini wrote:
Two vessels contain mixtures of milk and water in the ration of 4:9 in the 1st vessel and 2:7 in the 2nd vessel. In what ratio should the contents of these two vessels be mixed such that the resultant mixture has milk and water in the ratio of 2:5?

Is the volume of both vessels are same?
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Manager
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Re: PS Mixtures: Ratio of milk and water [#permalink]  10 Oct 2011, 03:02
gopu106 wrote:
maheshsrini wrote:
Two vessels contain mixtures of milk and water in the ration of 4:9 in the 1st vessel and 2:7 in the 2nd vessel. In what ratio should the contents of these two vessels be mixed such that the resultant mixture has milk and water in the ratio of 2:5?

Is the volume of both vessels are same?

no it's not same...since volume of milk and water in the vessels is not same..

You can solve this using alligation technique :

{2/7 -2/9 } / {4/13 - 2/7 } = 26/9.
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Re: PS Mixtures: Ratio of milk and water [#permalink]  11 Oct 2011, 22:52
hey

Can u guys explain why is this approach wrong ?

x units of mixture 1
y units of mixture 2

4x+2y / ( 9x+7y ) = 2/ 5

by this way , the prop is 2 :1
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Re: PS Mixtures: Ratio of milk and water [#permalink]  12 Oct 2011, 03:43
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4X/13 +2Y/9=2/7(X+Y)
solving it , we have - X/Y=26/9
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Re: PS Mixtures: Ratio of milk and water [#permalink]  26 Apr 2014, 19:34
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Re: PS Mixtures: Ratio of milk and water   [#permalink] 26 Apr 2014, 19:34
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