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# Two vessels contain mixtures of milk and water in the ratio of 4:9 in

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Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]

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16 Aug 2011, 17:16
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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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]

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16 Aug 2011, 23:07
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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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]

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17 Aug 2011, 00:30
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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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]

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17 Aug 2011, 06:32
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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]

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18 Aug 2011, 03:05
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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 10 Jan 2010 Posts: 117 GPA: 4 WE: Programming (Computer Software) Followers: 0 Kudos [?]: 105 [0], given: 33 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 08 Oct 2011, 17:41 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? _________________ -If you like my post, consider giving KUDOS Manager Status: Trying hard to give another shot! Joined: 29 Jun 2010 Posts: 114 GMAT 1: 610 Q45 V29 WE: Information Technology (Computer Software) Followers: 1 Kudos [?]: 39 [0], given: 50 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 09 Oct 2011, 03:09 What is the original Answer? _________________ Thanks, GC24 Please click Kudos ,if my post helped you Manager Joined: 21 Aug 2010 Posts: 189 Location: United States GMAT 1: 700 Q49 V35 Followers: 2 Kudos [?]: 88 [0], given: 141 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 09 Oct 2011, 03:26 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? _________________ ------------------------------------- Manager Status: Trying hard to give another shot! Joined: 29 Jun 2010 Posts: 114 GMAT 1: 610 Q45 V29 WE: Information Technology (Computer Software) Followers: 1 Kudos [?]: 39 [0], given: 50 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 10 Oct 2011, 04:02 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. _________________ Thanks, GC24 Please click Kudos ,if my post helped you Current Student Joined: 18 Mar 2011 Posts: 45 Schools: Foster '17 (A) Followers: 0 Kudos [?]: 6 [0], given: 25 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 11 Oct 2011, 23:52 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 Current Student Joined: 23 Oct 2010 Posts: 386 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Followers: 21 Kudos [?]: 284 [2] , given: 73 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 12 Oct 2011, 04:43 2 This post received KUDOS 1 This post was BOOKMARKED 4X/13 +2Y/9=2/7(X+Y) solving it , we have - X/Y=26/9 _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth GMAT Club Legend Joined: 09 Sep 2013 Posts: 11094 Followers: 511 Kudos [?]: 134 [0], given: 0 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 26 Apr 2014, 20:34 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 18 Jul 2013 Posts: 73 Location: Italy GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38 Followers: 1 Kudos [?]: 53 [0], given: 114 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 30 Aug 2014, 14:07 hi , i'm trying the allegation method, can someone tell me where i'm wrong? Vessel 1-----------------Vessel 2 4/9-----------------------2/7 --------------2/5------------- 4/35----------------------2/45 result : Vessel 1 / Vessel 2 = 18/7 Intern Joined: 20 Mar 2013 Posts: 11 GMAT 1: 570 Q46 V23 GMAT 2: 620 Q47 V28 Followers: 0 Kudos [?]: 2 [0], given: 8 Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 26 Nov 2014, 01:05 oss198 wrote: hi , i'm trying the allegation method, can someone tell me where i'm wrong? Vessel 1-----------------Vessel 2 4/9-----------------------2/7 --------------2/5------------- 4/35----------------------2/45 result : Vessel 1 / Vessel 2 = 18/7 try converting all ratios of milk to water into fractions of either water or milk V1 milk...................V2 milk 4/13...........................2/9 ................2/7.................. ??................................?? SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 37 Kudos [?]: 1660 [0], given: 193 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 26 Nov 2014, 02:05 mockingjay wrote: oss198 wrote: hi , i'm trying the allegation method, can someone tell me where i'm wrong? Vessel 1-----------------Vessel 2 4/9-----------------------2/7 --------------2/5------------- 4/35----------------------2/45 result : Vessel 1 / Vessel 2 = 18/7 try converting all ratios of milk to water into fractions of either water or milk V1 milk...................V2 milk 4/13...........................2/9 ................2/7.................. ??................................?? Perfect. This will the fastest method to calculate. We can also take into account portions of water for computation... answer would be the same V1 Water ................... V2 Water 9/13 ............................ 7/9 ................... 5/7 .............. ?? ................ .. ...............?? _________________ Kindly press "+1 Kudos" to appreciate Intern Joined: 08 Dec 2013 Posts: 47 Followers: 0 Kudos [?]: 0 [0], given: 23 Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 03 Mar 2015, 21:11 hey wats the problem with this.. 4x+2y/9x+7y=2/5 x=ratios of 1st cont y=ratios of 2nd cont Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6830 Location: Pune, India Followers: 1926 Kudos [?]: 11948 [0], given: 221 Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink] ### Show Tags 03 Mar 2015, 22:16 shreygupta3192 wrote: hey wats the problem with this.. 4x+2y/9x+7y=2/5 x=ratios of 1st cont y=ratios of 2nd cont What is 4x here? Why are you taking x to be ratio of 1st concentration? Do you mean to say that x is 4:9 because ratio of milk:water in first solution is given to be 4:9. So what quantity does 4x signify? What you can say is that volume of 1st solution = x and volume of second solution = y We know that Concentration of milk * Volume = Amount of milk So 4/13 * x = Amount of milk in solution 1 2/9 * y = Amount of milk in solution 2 Similarly for water. $$\frac{(4/13)*x + (2/9)*y}{(9/13)*x + (7/9)*y} = \frac{2}{5}$$ = Amount of milk in total solution/Amount of water in total solution (20/13)*x + (10/9)*y = (18/13)*x + (14/9)*y (2/13)*x = (4/9)*y x/y = 26/9 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]

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03 Mar 2015, 23:30
thanx..thats what i meant ..nice explanation.
Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in   [#permalink] 03 Mar 2015, 23:30
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