Rodrick mixes a martini that has a volume of 'n' ounces havi

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

Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:

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

Answer: C.
_________________

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.

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

Not sure if this is the method you're looking for but:

Verm Gin
40% 0%

25%

25 15

Which reduces to 5:3

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

Fluke/Bunuel, can you please explain this to me? I don't understand the equation 0.4n=0.25(n+g).
_________________

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.
_________________

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.

Thanks! This does help!
_________________

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 weighted averages formula, 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
_________________

mixture already has 60% gin, and we need 75%.

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

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

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..

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

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

ANSWER: C

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

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

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.
_________________

This is how I did it. It took me 1m 10 S:
For simplicity, start by assuming the gin has a volume of 100 units.

Current amount of vermouth: 40 units

I rephrased the question to say:
With the numerator being 40, what should the denominator be, so that the fraction becomes 1/4 (25% Vermouth)?
For what value of x will the ratio 40/x become 1/4?

A quick mental math will tell you x should be 160 (since 40*4=160)

Thus, we have created a condition where the question's requirement is satisfied.

Thus the amount of gin in the new mix will be =160-40=120
Of this 120, 60 was already present.
Thus he needs to add another 60 units of gin to make the mixture 25% Vermouth

However, the answer choices are in terms of n, the volume of the whole mix.

So lets convert 60 to terms of n.
We had started by assuming that the mix had 100 units for simplicity.
So what % of 100 is 60? easy its 60%

60% in fraction is 3/5.
Thus the answer should be 3n/5