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
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% VermouthHowever, 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