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

Question

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.

A. 26/9
B. 2
C. 17/9
D. 9/17
E. 9/26

Show Answer

Official Answer

A

A. 26/9
B. 2
C. 17/9
D. 9/17
E. 9/26

jamifahad · Accepted Answer

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

fluke · Answer

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}}

DeeptiM · Answer

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..

KarishmaB · Answer

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.

maheshsrini · Answer

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.

A. 26/9
B. 2
C. 17/9
D. 9/17
E. 9/26

Show Answer

Official Answer

A

gmatcracker24 · Answer

What is the original Answer?

g106 · Answer

Is the volume of both vessels are same?

gmatcracker24 · Answer

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.

LalaB · Answer

4X/13 +2Y/9=2/7(X+Y)
solving it , we have - X/Y=26/9

oss198 · Answer

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

mockingjay · Answer

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..................
??................................??

PareshGmat · Answer

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 ..............

?? ................ .. ...............??

shreygupta3192 · Answer

hey wats the problem with this..

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

x=ratios of 1st cont
y=ratios of 2nd cont

KarishmaB · Answer

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

shreygupta3192 · Answer

thanx..thats what i meant ..nice explanation.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards