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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Fri Apr 01, 2011 7:40 pm

Jug contains water and orange juice in the ratio 5:7 . another jug contains water and orange juice in ratio 7 : 2 . In what proportion should these 2 liquids be mixed to give a water and orange juice in ratio 3 : 4

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Source: Beat The GMAT — Problem Solving | Fri Apr 01, 2011 7:40 pm

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Fri Apr 01, 2011 8:02 pm

The question lacks sufficient information.

Assumptions have to be made that both jugs are of similar size and are up to the brim with the mixture.

Vineesh,
Just telling you what I know and think. I am not the expert.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Apr 01, 2011 8:11 pm

diebeatsthegmat wrote:Jug contains water and orange juice in the ratio 5:7 . another jug contains water and orange juice in ratio 7 : 2 . In what proportion should these 2 liquids be mixed to give a water and orange juice in ratio 3 : 4

First determine the fraction of water in each part, using a common denominator:
Fraction of water in jug 1 = 5/12 = 105/252.
Fraction of water in jug 2 = 7/9 = 196/252.
Fraction of water in mixture = 3/7 = 108/252.

Now we can use perform alligation with just the numerators:

The proportion needed of each ingredient in the mixture = the positive distance between the OTHER 2 numerators.

Jug 1:
Proportion needed of jug 1 = 196 - 108 = 88.

Jug 2:
Proportion needed of jug 2 = 108 - 105 = 3.

Ratio:
Jug 1 : Jug 2 = 88:3.

Last edited by GMATGuruNY on Tue Feb 07, 2012 7:11 am, edited 1 time in total.

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gmat1978: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Thu Dec 23, 2010 7:38 pm

by gmat1978 » Sun Apr 03, 2011 9:58 am

@Mitch:

I am unable to follow the below explanation. Can you please help / elaborate.

Thanks

GMATGuruNY wrote:Using alligation:
The proportion needed of starting fraction = the positive difference between the other 2 fractions.

Jug 1:
Proportion needed of the 5/12 liquid = 196/252 - 108/252 = 88/252.

Jug 2:
Proportion needed of the 7/9 liquid = 108/252 - 105/252 = 3/252.

Ratio:
Jug 1 : Jug 2 = (88/252) : (3/252) = 88:3.

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Mon Apr 04, 2011 7:44 am

Let X be volume of mixture 1 and Y be volume of mixture 2
I II
W O W O
5X/12 7X/12 7Y/9 2Y/9

Combine the 2 mixtures. Add the water parts and orange parts and form the required ratio

(5X/12 + 7Y/9 )/(7X/12 + 2Y/9) =3/4

20x/12 +28y/9 =21x/12 + 6y/9 ( Cross multiply but don't Simplify anything!!)

X/12=22Y/9 ( Rearrange )
X/Y =88/3

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