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Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]

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28 Dec 2009, 13:18

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Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

Guys, please help me out. I want to know how to solve this question using the Allegation method. I know the other way(using equations) but I need to understand the Allegation method.

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

Re: Method of Allegation in Percentages [#permalink]

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28 Dec 2009, 15:35

Bunuel, thanks for the solution but as i said, i already know the "equations" method. The problem is that I cant solve it using the Allegation method. Any help on that would be nice.

Re: Method of Allegation in Percentages [#permalink]

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13 Jul 2010, 05:48

I want to respond to the following question appearing in this forum: _____ Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

A) n/6 B) n/3 C) 3n/5 D) 5n/6 E) 8n/5 _____

The answer C) 3n/5 for Gin is obviously not correct for the following reason. Gin's concentration is 60% which is much higher than that of Vermouth (40%). Obviously, you need less of Gin than Vermouth to make n quantity of Martin. Consequently, the answer we should be looking for must be below 1/2 of the quantity of the total (n). The correct proportional volume of Gin is 3n/10 using the Alligation Method. Make a nine cell table like the one below (Unfortunately, I can't draw the table here. I have added starred lines to space the figures to create a Table image). Obtain diagonal differences and enter them as shown in top right and bottom right boxes(always positive numbers). Add right hand column (15+35=50). Calculate amount of Gin proportion as (n/50)*15 =3/10 n. Calculate amount of Vermouth proportion as (n/50)*35 =7/10 n

Re: Method of Allegation in Percentages [#permalink]

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22 Jul 2011, 05:02

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Dear Friends,

Using allegations we will view the action that Rodrick performs as below:

"He will Mix Martini [60 % gin by volume ] with Gin [ 100 % gin by volume] to yield a martini [75 % gin by volume]."

By the method of allegations : If we have 2 quantities to mix ,one with higher percentage H and other with lower percentage L ,to get a desired solution R %we proceed as Percentage of Lower in final Result = H-R Percentage of Higher in final Result = R-L.

Therefore using the allegations method we have %volume of Pure Gin required = 75 -60 = 15 %volume of Martini (60 % gin)required = 100 -75 =25

Which reduces to Pure Gin to Martini =3 :5. Which can be inferred as for every 5 ml of martini if we should add 5 ml of pure gin to get a drink that is 75 % gin and 25 % Vermouth by volume.

So , we have : For 5 ml Martini we need 3 ml Gin For 1 ml martini we need 3/5 ml of Gin For 'n' ml of martini we need 3n/5 ml of Gin.

Re: Method of Allegation in Percentages [#permalink]

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18 Sep 2011, 01:45

Bunuel wrote:

gaurav05nov wrote:

Guys, please help me out. I want to know how to solve this question using the Allegation method. I know the other way(using equations) but I need to understand the Allegation method.

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

Re: Method of Allegation in Percentages [#permalink]

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18 Sep 2011, 09:02

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total V G 1 ounce 0.4 0.6

n ounce 0.4n 0.6n -------------initial expression

lets say g ounces of gin is added to this mixture

n+g 0.4n 0.6n+g --------------final expression

given that after adding g ounces of gin , V should become 25% of the total volume.

=>Volume of V/total volume = 25/100

=> 0.4n /n+g = 1/4

=> 1.6n = n+g

=> g = 3n/5

Answer is C.

petrifiedbutstanding wrote:

Bunuel wrote:

gaurav05nov wrote:

Guys, please help me out. I want to know how to solve this question using the Allegation method. I know the other way(using equations) but I need to understand the Allegation method.

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

Guys, please help me out. I want to know how to solve this question using the Allegation method. I know the other way(using equations) but I need to understand the Allegation method.

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

He wants to mix a martini of 60% Gin with a liquid that is 100% Gin to give a mixture with 75% Gin (because 25% is Vermouth) Using the mixtures formula discussed here (http://www.veritasprep.com/blog/2011/03 ... -averages/), we get, w1/w2 = (100 - 75)/(75 - 60) = 5:3 Martini:Pure Gin must be added in the ratio 5:3. So if martini is n, pure gin must be (3/5)n

Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]

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09 Sep 2013, 01:30

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gaurav05nov wrote:

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

A) n/6 B) n/3 C) 3n/5 D) 5n/6 E) 8n/5

Initially Martini = V : G = 4 : 6 = 2 : 3 Ratio required is = 25 : 75 = 1 : 3 Since V is same hence ratio should be 2 : 6 Hence 3 parts of gin should be added to the initial mixture i.e. same as what was in the initial mixture i.e. 60n/100 = 3n/5

The mixture related problems if dealt with ratios becomes much easier..

Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]

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16 Dec 2013, 06:52

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gaurav05nov wrote:

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]

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13 Jan 2015, 07:27

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Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]

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13 Jan 2015, 07:50

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PROBLEM: Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

A) n/6 B) n/3 C) 3n/5 D) 5n/6 E) 8n/5

SOLUTION:

A quick way to calculate without any algebra is:

(Old - New)/(New) i.e. (40-25)/(25) = 3/5 i.e. Martini should be diluted 3/5 times

Re: Rodrick mixes a martini that has a volume of 'n' ounces havi [#permalink]

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30 Dec 2015, 07:12

HI Karishma

Is this approach also right (from one of your posts)?

Volume (initial) x concentration (initial) = Volume (final) x Concentration (final) Since, the volume of Vermouth remains same (not Gin), this should be applied to Vermouth Therefore, n x 40% = Volume (final) x 25% Volume (final) = 8n/5

So, solution added = (8n/5) - n ==> 3n /5

VeritasPrepKarishma wrote:

gaurav05nov wrote:

Guys, please help me out. I want to know how to solve this question using the Allegation method. I know the other way(using equations) but I need to understand the Allegation method.

Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?

He wants to mix a martini of 60% Gin with a liquid that is 100% Gin to give a mixture with 75% Gin (because 25% is Vermouth) Using the mixtures formula discussed here (http://www.veritasprep.com/blog/2011/03 ... -averages/), we get, w1/w2 = (100 - 75)/(75 - 60) = 5:3 Martini:Pure Gin must be added in the ratio 5:3. So if martini is n, pure gin must be (3/5)n

Is this approach also right (from one of your posts)?

Volume (initial) x concentration (initial) = Volume (final) x Concentration (final) Since, the volume of Vermouth remains same (not Gin), this should be applied to Vermouth Therefore, n x 40% = Volume (final) x 25% Volume (final) = 8n/5

So, solution added = (8n/5) - n ==> 3n /5

Yes, correct. Since amount of Vermouth stays the same in the two cases, Volume of solution*Concentration of Vermouth should be equal in the two cases.
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