Darla decides to mix lemonade with limeade to make a new drink

You can use allegation.

To use allegation you relate the weighted averages of percentages of the ingredients to the ratio of the parts of the mixture.

For example if you use a 1:1 ratio of the two parts of the mixture, then the weighted average of the percentages of the ingredients will be the mean of the percentages found in the two parts. in other words, in a 1:1 mixture the weighted average of the percentages will be exactly halfway between the percentages found in each of the ingredients.

The mixture is to contain more than 45% water.

45% is the mean of the percentages of water found in the two parts, lemonade, which contains 50% water, and limeade, which contains 40% water. So a mixture containing a 1:1 ratio of lemonade to limeade would contain 45% water.

Since the mixture is to contain more than 45% water, it must contain more lemonade than limeade.

Eliminate answer choices D and E.

The mixture is also to contain more than 24% sugar. 24% is 1/3 of the way from 20%, the proportion of sugar in lemonade, to 32%, the proportion of sugar in limeade. So to get a sugar percentage greater than 24%, we need the mixture to be more than 1/3 limeade.

A indicates that limeade is 1/4 of the mixture. 1/4 < 1/3. Eliminate A.

B indicates that limeade is 3/10 of the mixture. 3/10 < 1/3. Eliminate B.

C indicates that limeade is 2/5 of the mixture. 2/5 > 1/3.

The correct answer is .

Bunuel can you please explain this further

Can you please be a little bit more specific? Thank you.

Apologies! I figured out where I was going wrong

Let Lemonade be LE, Limeade be LI and Citrusade be CI.
So, it can be represented as below.

Water Juice Sugar
LE 50% 30% 20%
LI 40% 28% 32%
CI >45% .... >24%

Now we will use mixture formula.

Let LE/LI be x/y in the mixture CI.
x/y > (45-40)/(50-45). since >45 means skewed towards 50% i.e. LE
x/y >1

Similarly,

x/y <(32-24)/(24-20). Since >24 is skewed towards 32% i.e. LI
x/y <2

So, 1<x/y<2

Only C option satisfies this condition.

I used method of elimination and weighted averages (sort of):
Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?

(A) 3 : 1
(B) 7 : 3
(C) 3 : 2
(D) 4 : 5
(E) 3 : 4

I took a case : 46% water and 25% sugar (as per condition above) --> this would mean more water is overall contributed by lemonade and sugar would be more contributed by limeade. (more than 25% sugar) --> but the water content isn't overwhelmingly high (almost like 46% water, 25% sugar and rest juice = 1/2 water, 1/4th sugar rest juice) --> eliminate A and B
D and E state the opposite --> meaning water content would lower (in comparison to sugar -- sugar content at an average would increase)
This leaves us C which can result in 46% water and 25% sugar

Using allegation :

Let conc. of water in citrusade be 46%
40.........46.........50
W(lemonade)/W(limeade) = 4/6 = 2/3

Ans. : c

Let, L for lemonade, l for limeade, C for citrusade
Given ratios for water, lemon juice, and sugar
L = 50 30 20
l = 40 28 32
C = >45 __ >24

Weighted Average formulae = W1/W2 = (A2 - Aavg) / (Aavg - A1)

Since water in Citrusade is >45, let us consider 46

Hence, L/l = (50 - 46) / (46 - 40)
L/l = 4 / 6 = 2 / 3

Option C

Lemonade: 50% water, 20% sugar, 30% lemon juice
Limeade: 40% water, 32% sugar, 28% lime juice

Citrusade:
>45% water (implies lemonade is more than 1/2. Options (D) and (E) are out)
> 24% sugar
If sugar were exactly 24%, ratio of lemonade/limeade = (32 - 24)/(24 - 20) = 8:4 = 2:1 i.e. lemonade would be 2/3rd of total. But since sugar is more than 24%, lemonade is less than 2/3.

Check for option (C) which has more than 50% lemonade but the least of the leftover 3 options. Option (C) has 3/5 = 9/15 lemonade. This is less than 2/3 i.e. 10/15.
Answer (C)

Citrusade is more than 45% water.
Since the water percentage for citrusade (over 45) is closer to the water percentage for lemonade (50) than to the water percentage for limeade (40), the lemon-lime ratio must be weighted toward lemonade.
Eliminate D and E, which are weighted toward limeade.

Citrusade is more than 24% sugar.
Let the total amount of citrusade = 100 pounds, implying that the amount of sugar must be more than 24 pounds.

The remaining ratios imply the following:
A --> limeade = 1/4 of the mixture
B --> limeade = 3/10 of the mixture
C --> limeade = 2/5 of the mixture
Test B.

B: lemonade:limeade = 7:3, implying 70 pounds of lemonade and 30 pounds of limeade
Since lemonade is 20% sugar and limeade 32% sugar, the total amount of sugar = (0.2)(70) + (0.32)(30) = 14 + 9.6 = 23.6 pounds
The amount of sugar is too small, implying that limeade -- which has the higher percentage of sugar -- must constitute a greater proportion of the mixture.
Only C is viable.

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