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

Question

On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day?

A. $0.15
B. $0.20
C. $0.30
D. $0.40
E. $0.45

A. $0.15
B. $0.20
C. $0.30
D. $0.40
E. $0.45

Bunuel · Accepted Answer

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 # of glasses of orangeade made on the second day is 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.

Answer: D.

Hope it's clear.

yogeshwar007 · Answer

Bunuel

Is it ok to plugin for this sum.

100 ltrs of the orangeade= 50 W + 50 Concentrate
150 ltrs of the orangeade-= 100W + 50 concentrate

since total revenue is the same
100*.6 = 150* x
thus x = 0.4

Can i take the above approach?

gnan · Answer

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

jlgdr · Answer

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

kanusha · Answer

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

Bunuel · Answer

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.

ScottTargetTestPrep · Answer

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.

KarishmaB · Answer

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)

dave13 · Answer

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

KarishmaB · Answer

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

GMATGuruNY · Answer

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.

D

avigutman · Answer

Video solution from Quant Reasoning starts at 0:27 Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=cx-mlMq7TGI

quetzalferry · Answer

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

Hitesh0701 · Answer

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.

sayan640 · Answer

we can use alligation to solve this problem.
Let P be the cost of orange juice.

.60 is the cost of orange juice solution on the first day.
The cost of water = zero.
The amount of orange = the amount of water = 0

P----------------.60 -----------------0
x---------------.60---------------x

(p-.6 )/ x = .6 - 0 ) / x
p=1.2

The cost of orange juice on the second day = (x*p + 0*2x ) / 3x = 1.2 / 3 = .4

D is the answer.
Attached is the diagram.
 KarishmaB   chetan2u   GMATinsight  please check.

KarishmaB · Answer

I am not sure why and how you have used allegation here. We cannot get the cost of orange juice. All we are given is the selling price of a cup of the mix on day 1. No profit, nothing. The question is a lot simpler. Check here: https://gmatclub.com/forum/on-a-certain ... l#p1686273

rushimehta · Answer

Bunuel   KarishmaB   chetan2u   avigutman   MartyMurray

Are we assuming here that the "quantity of orange juice/glass" is the same on Day 1 and Day 2 ???

KarishmaB · Answer

Yes, it is a fair assumption. When you sell a 'glass of orange juice,' you sell a full glass. You cannot vary the quantity and still call it a 'glass of orange juice.'

MartyMurray · Answer

Sometimes, in answering GMAT Quant questions, we have to ask ourselves "What must this mean?" In such cases, we have to use context clues to confirm the exact meaning of what's presented.

In this case, we can use the way the word "glass" is used and the format of the question to determine whether we should assume that a "glass" is a constant quantity.

The first clue we have in this case is that the passage mentions the price per "glass." We see that the question is using "glass" to indicate a particular quantity of orange juice. We are not told what exactly that quantity is, but it appears that we should presume that it is the same quantity in both cases.

The second clue is that, if the quantity per glass were not assumed to be the same, then there would be no way to answer the question because, in that case, any positive value would be a possible answer.

So, using those clues, we can confirm that we should assume that "glass" represents a constant quantity.

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

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