Averages Question

[sukhman]

Two vessels contain milk solutions , with milk and water in the ratio 2:11 in the 1st vessel and in the ratio of 5:9 in the second . In what ratio should the contents of these two vessels be mixed such that resultant mixture has milk and water in the ratio 3:8 ?

[theCodeToGMAT]

First vessel
Milk = 2x
Water = 11x

Second Vessel
Milk = 5y
Water = 9y

(2x + 5y) / (11x + 9y) = 3:8

16x + 40y = 33x + 27y
13y = 17x

x : y = 13 : 17

So, Vessel 1 : Vessel 2 = 169 : 238

Is this the Answer?

[sukhman]

169:238

[theCodeToGMAT]

169:238

Yep correct

[GMATGuruNY]

For an alternate approach to this sort of problem, check my posts here:

https://www.beatthegmat.com/mixture-t223876.html
https://www.beatthegmat.com/ratios-fract ... tml#484583 (two posts)
https://www.beatthegmat.com/mixtures-t210709.html
https://www.beatthegmat.com/mixture-rati ... 89861.html

[mevicks]

Alligation approach: (a.k.a Mitch's shortcut approach to such problems - refer his posts in the above links. They are all just too brilliant! )

Vessel 1 (V1) :
M/W --> 2/11
M__________________W
2/13-------------------11/13

Vessel 2 (V2) :
M/W --> 5/9
M__________________W
5/14--------------------9/14

Final Mix M3:
M/W --> 3/8
M__________________W
3/11--------------------8/11

Consider the proportion of Milk in the final mixture:
MV1___________M3M_________MV2
2/13---------------3/11--------------5/14

Make the denominators same by taking the LCM throughout:

MV1__________________________M3M_______________________MV2
2*11*14/11*13*14-----------3*13*14/11*13*14-----------5*11*13/11*13*14

Thus,
V1/V2 = [ (5*11*13 - 3*13*14)/11*13*14 ] / [ (3*13*14 - 2*11*14)/11*13*14 ] = [spoiler]169/238[/spoiler]