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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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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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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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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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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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