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

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.

I hope the solution helps as a good reference.

Cheers,
Rohan

Any response as to how to solve the problem using Allegation method would be useful.
Please help!!

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

60(Gin)****************************15(40-25)
*******************25(Martin)
40(Vermouth)***********************35(60-25)


Mathew

I will try.
Volume of martini given = n
Volume of vermouth in martini = 40% of n = 0.4n


Let "g" be the volume of gin we add.
New Volume of martini = n+g
Also, we did not add any vermouth.
New Volume of vermouth = 0.4n (still same as old)

New volume of vermouth= 25 % New martini (n+g)

0.4n=0.25(n+g)
n=3n/5

Pick number and see. It will be clear.
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Thanks! This does help!
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mixture already has 60% gin, and we need 75%.

\(\frac{0.6n + x}{n + x} = 0.75\)

\(x = \frac{3}{5}n\)
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Way I did it

Smart Numbers

n=100

So we'll have 60+x/100+x=3/4
x=60

So 60/100 = 3/5n

Answer is C

Hope it helps!
Cheers!
J

Place n = 1 in the question as well as in OA & say "x" volume of Gin is added.

Equation setup would be as follows:

\(\frac{25}{100}(1+x) = \frac{40}{100}\)

\(x = \frac{3}{5}\)

Answer = C
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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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