On a certain day, orangeade was made by mixing a certain

Let the amount of orange juice be X.

Orangeade made on first day = X + X(same amount of water) = 2X

Orangeade made on second day = X + 2X (twice the amount of water) = 3X

So the total number of glasses made will be of the ratio 2:3

As total revenue is same on both days,

(2)(0.16) = (3)(Price on second day)

Price per glass on second day = 0.32/3 = 0.107

I really like this one

So first you sold 1:1 water and orange, let's say a liter of each so total per glass is 2 liters
After you sold 2:1 water and orange, let's say a liter of each again so total per glass is 3 liters

Now since the revenue is the same and the ratio in the quantity increased to 3/2 then the price has to be the inverse 2/3

So 0.6 * 2.3 - 0.4

Answer is D

Hope it clarifies
Cheers
J

On fist day 0.60$ per glass and assume sold 10 glasses of orange = 6$
On next Day on adding double amount of water, might sold 20 glasses of orange , so 0.30$ x 20 = 6 $
So C
But My answer is wrong... Even i understood Above solutions, But why analysis is wrong
Pls help

On the first day orangeade was made by mixing a certain amount of orange juice with an equal amount of water. So, if 10 glasses of orangeade was sold on the first day, then it was made by mixing 5 glasses of orange juice with 5 glasses of water.

On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water, so it was made with 5 glasses of orange juice and 10 glasses of water, which makes total of 15 glasses of orangeade.

10*0.6 = 15*x --> x = 0.4.

Hope it's clear.

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.

Answer D.

Revenue = Number of glasses * Price per glass

On second day, twice the amount of water was added so number of glasses was 3/2 the number of glasses on first day. Revenue on both days was the same so

N * 0.6 = (3N/2) * Cost on day 2

Cost on day 2 = 0.4

Answer (D)

why is my reasoning wrong UPDATE I noticed one mistake, so I corrected it but still dont get how to reach final solution

first day: 1 litre of juice +1 litre of water hence ratio---> 1:1 (total 2 litres)

Second day: 1 litres of juice +2 litres of water hence ratio---> 1:2 ( total 3 litres )


If ratio of mixture on day one to mixture on day two is 2 to 3 and price per glace on day one is 0.60

so i assume from this ratio \(2:3\) that \(2\) is 0.60 and what to do next if \(2\) is 0.60 then what is \(3\) how to calculate

or where am i wrong

Note that Revenue is the same on both the days. That is the information that will give you the relation between 2:3 and 0.60.

Revenue = Unit Price * Volume sold

UnitPrice1 * VolumeSold1 = UnitPrice2 * VolumeSold2

VolumeSold1 / VolumeSold2 = UnitPrice2 / UnitPrice1

2/3 = UnitPrice2 / 0.60

UnitPrice2 = 0.40

Plug in values in terms of GLASSES.

On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water.
The orangeade was sold at $0.60 per glass on the first day.
Let the total orangeade = (1 glass juice) + (1 glass water) = 2 glasses.
Since each glass sells for 60 cents, the revenue = 2*60 = 120 cents.

On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water.
Orangeade = (1 glass juice) + (2 glasses water) = 3 glasses.

The revenue from selling the orangeade was the same for both days.
What was the price per glass on the second day?
Since the revenue for the 3 glasses on the second day remains 120 cents, the price per glass \(= \frac{120}{3} = 40\) cents.

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First Post!
Saw this question on the 2024-2025 GMAT online question bank. None of the answers for this question seem to make sense to me. Hoping this will click with someone

Formula First:
Selling Price = Profit - Cost
Since Profit isn't mentioned, we can deduce the correlation between selling price and cost
Selling price = - Cost

Note: Also good to know:
Revenue = Profit - Total Cost
Selling Price * Total number of Units = Revenue
Cost * Total number of Units = Total Cost

First day one cup cost: 1/2 => 50% of orange juice
Selling Price = 0.6
Cost = C

Second day one cup cost: 1/3 => 33% of orange juice => 33%/50% amount of orange juice relative to day 1 = 1/2/1/3 = 2/3 C (where C is day 1 cost)
Selling Price = X (trying to solve for this)
Cost = 2/3C

Putting the two formulas together
Day 1 => 0.6 = - C
Day 2 => X = -2/3C

Find the ratio: (day 1 / day 2)
Day 1 / Day 2 = 0.6/X = -C/(-2/3C)
=> 0.6/X = 3/2
=> 0.6 = 3/2 * X
=> 0.6 / 3/2 = X
=> 0.6 * 2/3 = X
=> X = 0.4

­We can solve this question by following this strategy:
For example,
We sold 200 units of orangeade on day 1 @ 0.6/ unit which comes to 120 (revenue)
Revenue is same for both the days and hence we sold 300 units @ x/unit which comes to 120(revenue is same for both the days)
Hence, 300*x=120
x=0.40

Hope this helps.