Dessert Recipe Mixture

[nikhilgmat31]

A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to
make a particular sauce. A chef accidentally makes 15 cups of the sauce with
40% melted chocolate and 60% raspberry puree instead. How many cups of
the sauce does he need to remove and replace with pure melted chocolate to
make the sauce the proper 50% of each?
(A) 1.5
(B) 2.5
(C) 3
(D) 4.5
(E) 5

[prasannakarthik]

Let's assume each cup is of 100 ml and that there are 15 such cups. Hence the final mixture has to have 750 ml of melted chocolate and 750 ml of raspberry puree. However, with 60% of puree added, there would be 600 ml of melted chocolates and 900 ml of raspberry puree. Hence, we need to remove 150 ml of raspberry puree and add 150 ml of melted chocolate; but suffice to concentrate on just removing raspberry puree, for replacement with melted chocolate will happen by default. So to remove 150 ml of raspberry puree, we need to remove 60 ml X x cups. Hence x = 2.5. This also means 100 ml of melted chocolate will also be removed. However, with addition of 250 ml of melted chocolates, the total quantity of melted chocolate gets adjusted to 750 ml. Hence answer is B.

[GMATGuruNY]

A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to
make a particular sauce. A chef accidentally makes 15 cups of the sauce with
40% melted chocolate and 60% raspberry puree instead. How many cups of
the sauce does he need to remove and replace with pure melted chocolate to
make the sauce the proper 50% of each?
(A) 1.5
(B) 2.5
(C) 3
(D) 4.5
(E) 5

Chocolate percentage in the botched sauce: 40%.
Chocolate percentage in the pure chocolate: 100%.
Chocolate percentage in the MIXTURE of botched sauce and pure chocolate: 50%.

Let S = the botched sauce and C = the pure chocolate.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with percentages for the sauce and the chocolate on the ends and the percentage for the mixture in the middle.
S 40%-----------50%-----------100% C

Step 2: Calculate the distances between the percentages.
S 40%----10-----50%----50-----100% C

Step 3: Determine the ratio in the mixture.
The required ratio of sauce to chocolate is equal to the RECIPROCAL of the distances in red.
S:C = 50:10 = 5:1.

Since 1 cup of pure chocolate is required for every 5 cups of botched sauce, the pure chocolate must constitute 1/6 of the 15 cups:
(1/6)(15) = 2.5.

The correct answer is B.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

[nikhilgmat31]

Thanks Mitch,

I was able to solve this question but with a little longer approach of equations

[[email protected]]

Hi All,

This question can be solved by TESTing THE ANSWERS.

To start, we're told that 15 cups of 'sauce' are made up of 40% chocolate and 60% raspberry. This gives us...

Total = 15 cups
Choc = 40%(15) = 6 cups
Rasp = 60%(15) = 9 cups

We're told to remove a certain amount of the mixture and replace it with PURE chocolate, so that the mixture becomes a 50/50 chocolate/raspberry mix. In simple terms, we need the total amount of Chocolate to be 7.5 CUPS. We're asked for the number of cups of the mixture that would have to be replaced. Let's TEST THE ANSWERS.

While it's mathematically advantageous to TEST answer B or D first, Answer C seems like easier math...

IF... we remove 3 cups of sauce, those 3 cups are....
40%(3) = 1.2 cups Choc
60%(3) = 1.8 cups Rasp

The number of cups of Choc can be calculated by using the original number of cups (6), subtracting the amount removed when we remove the sauce (in this case, 1.2), then adding back the pure chocolate that replaces the removed sauce (in this case, 3) = 6 - 1.2 + 3 = 7.8 cups chocolate. This is TOO MUCH chocolate (we wanted it to be 7.5 cups), but it's fairly close, so we're likely looking for an answer that is CLOSE to 3....Let's TEST Answer B...

IF... we remove 2.5 cups of sauce, those 2.5 cups are....
40%(2.5) = 1 cup Choc
60%(2.5) = 1.5 cups Rasp

Choc = 6 - 1 + 2.5 = 7.5 cups chocolate. This is EXACTLY what we're looking for, so this MUST be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich