On a certain day, orangeade was made by mixing a certain amount of orange juice GMAT Problem Solving

We are given that orangeade is made on Day 1 with an EQUAL AMOUNT of water and orange juice. We can set this information up into a ratio using a variable multiplier:

W : OJ = x : x

Thus, orangeade quantity = amount of water + amount of OJ = x + x = 2x

We are next given that orangeade on Day 2 was made by mixing the same amount of orange juice with twice the amount of water. We can set this information up into a ratio using a variable multiplier:

W : OJ = 2x : x

Thus, orangeade quantity = amount of water + amount of OJ = 2x + x = 3x

We also know that all orangeade made was sold and that the revenue on both days was the same. We can therefore set up the following equation:

Day 1 Revenue = Day 2 Revenue

That is,

(quantity sold Day 1)(price per glass Day 1) = (quantity sold Day 2)(price per glass Day 2)

Let a be the amount of orangeade a glass can hold, then

quantity sold Day 1 = the number of glasses of orangeade sold on Day 1 = 2x/a

Similarly,

quantity sold Day 2 = the number of glasses of orangeade sold on Day 2 = 3x/a

We also know that the price per glass on day 1 = $0.6

But we don’t know the price per glass on day 2, so let’s label it as variable p.

We now have:

(2x/a)(0.6) = (3x/a)(p)

Multiplying both sides by a, we have:

(2x)(0.6) = (3x)(p)

1.2x = 3xp

1.2 = 3p

p = 0.4

Thus, each glass of orangeade was sold for $0.40 on Day 2.

Correct option: D

Let each glass = 1 unit.

First day:

Let water = 1 unit and juice = 1 unit.

Glasses = water + juice = 1+1 = 2.

Since each glass earns 60 cents, revenue = 2 x 60 = 120.

Second day:

Revenue = 120 (same as on the first day).

Since twice as much water is used, water = 2 units.

Juice = 1 unit (same as on the first day.)

Glasses = water + juice = 2+1 = 3.

Price per glass = revenue/glasses = 120/3 = 40.

Correct option: D

On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;

On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;

So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # glasses of orangeade made on the second day are 2 to 3.

We are told that "the revenue from selling the orangeade was the same for both days" so the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.

Say the price of the glass of the orangeade on the second day was $x then:

2 * 0.6 = 3 * x

x = $0.4

Correct option: D