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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]  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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]  18 Aug 2011, 02:05
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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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Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]  09 Oct 2011, 02:09
What is the original Answer?
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Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#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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Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#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: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]  26 Apr 2014, 19:34
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Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]  30 Aug 2014, 13:07
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
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Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]  26 Nov 2014, 00:05
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..................
??................................??
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Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]  26 Nov 2014, 01:05
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 ..............

?? ................ .. ...............??
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Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]  03 Mar 2015, 20:11
hey wats the problem with this..

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

x=ratios of 1st cont
y=ratios of 2nd cont
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Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]  03 Mar 2015, 21:16
Expert's post
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
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Re: Two vessels contain mixtures of milk and water in the ratio of 4:9 in [#permalink]  03 Mar 2015, 22:30
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, 22:30
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