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Allegation on 3+ values?

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Intern
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Joined: 18 Sep 2011
Posts: 11
Location: Canada
Concentration: Strategy, General Management
GMAT Date: 11-29-2011
WE: Corporate Finance (Retail)
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Allegation on 3+ values? [#permalink] New post 02 Oct 2011, 13:32
Hi,

I've just learned the allgegation method for weighted average/mixture questions and it is very fast when computing mixture questions with two different values!
Does anyone know if this method works for 3 or more values?
If so, how?

Thanks
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Re: Allegation on 3+ values? [#permalink] New post 02 Aug 2013, 02:20
In what ratio must a person mix three kinds of metal costing Rs.60/kg, Rs.75/kg and Rs.100 /kg so that the resultant alloy when sold at Rs.96/kg results in a gain of 20%?
(1) 1 : 2 : 4 (2) 3 : 7 : 6 (3) 1 : 4 : 2 (4) 1 : 4 : 1

Correct Answer - (3)

How can we solve this as it involves 3 quantities ?
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Re: Allegation on 3+ values? [#permalink] New post 02 Aug 2013, 02:43
Hi,

Happy to help

The fastest way would be to plug in the values in the options:

1. gives (60*1+75*2+100*4)/7=610/7

2. gives (60*3+75*7+100*6)=1205/7

3. gives (60*1+75*4+100*2)=560/7

4. gives ((60*1+75*4+100*1)=460/7

Now, desired rate= Rs. 80. So option 3.

In case you are interested in a detailed mathematical solutioning, substitute the basic ratio as "x"

Thus in option 1, the ratios would be x, 2x and 4x and so on in the other options



Regards

Argha
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Re: Allegation on 3+ values? [#permalink] New post 02 Aug 2013, 06:47
Yes, agreed that plugging in the choices is the best method but using allegation technique to find ratios of metals
M1 : M3= 1 : 1 and M2 : M3 = 4 : 1 so according to that M1 : M2 : M3 = 1: 4 : 1 should be the ratio of metals in the alloy ... could you point out what i'm missing ??
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Re: Allegation on 3+ values? [#permalink] New post 02 Aug 2013, 09:31
Hi,

Sorry but did not understand your question.

Why are you assuming this: M1 : M3= 1 : 1 and M2 : M3 = 4 : 1???


Regards

Argha
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Re: Allegation on 3+ values? [#permalink] New post 02 Aug 2013, 22:19
argha wrote:
Hi,

Sorry but did not understand your question.

Why are you assuming this: M1 : M3= 1 : 1 and M2 : M3 = 4 : 1???


Regards

Argha


M1 = metal costing 60/kg , M2 = metal costing 75/ kg and M3= 100/ kg.
sp = 96
profit = 20%
thus cp = 96/1.2 = 80

Using allegation, M1 : M3 = (100-80)/(80-60) = 20/20= 1:1
similarly, M2 : M3 = (100-80)/ ( 80-75) = 20/5 = 4: 1

Thus, M1 : M2 : M3 = 1: 4 : 1
where am i wrong ?
Re: Allegation on 3+ values?   [#permalink] 02 Aug 2013, 22:19
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