On a certain day, orangeade was made by mixing a certain : Problem Solving (PS)

**macjas** · Updated on: Jul 16, 2021

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

Spoiler: OA

Last edited by Bunuel on 16 Jul 2021, 12:16, edited 1 time in total.

Edited the question.

**Bunuel** · May 25, 2012

macjas wrote: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

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** · Jun 3, 2012

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** · Jun 7, 2012

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** · Feb 5, 2014

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** · Aug 23, 2014

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** · Aug 23, 2014

kanusha wrote: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

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.

**pate13** · Dec 13, 2014

I also like this question. I just wanted to post another way to think about this question.

The first day was a ratio of 1:1, which gives a total of 2 parts: 1L + 1W = 2X
The second day was a ratio of 1:2, which gives a total of 3 parts: 1L + 2W = 3X

Since the revenue was the same for both says, and since there was a quantity increase of 50% (3 is an increase of 50% from 2), you can think of the answer this way:

What number when increased by 50% equals .6? That number is .4

Also, as previously mentioned, since the increase was 3/2, you can also multiply .6 by 2/3, which is the inverse of 3/2. Admittedly, this method is probably better. I just wanted to point out a different method / different way to think about the problem.

**mathivanan** · Aug 14, 2015

macjas wrote: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

1o +1w = 2j*0.60=1.20
1o + 2w= 3j*0.40=1.20
the correct option is D

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**mcelroytutoring** · Updated on: Dec 7, 2016

Attached is a visual that should help. Part of the key here is realizing that a "glass" is a constant, and that you can insert numbers to "make it true".

Attachments

: Screen Shot 2016-12-07 at 7.06.07 PM.png (144.29 KiB) Viewed 27913 times
Open

Last edited by mcelroytutoring on 07 Dec 2016, 20:08, edited 5 times in total.

**KarishmaB** · May 18, 2016

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**dave13** · Apr 8, 2018

macjas wrote: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

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

that

is 0.60 and what to do next

if

is 0.60 then what is

how to calculate

or where am i wrong

**KarishmaB** · Apr 9, 2018

Karishma
Owner of Angles and Arguments

Check out my Blog Posts here: Blog

For Study Modules, click here: Study Modules
For Private Tutoring, contact us: Private Tutoring

**jalice** · Aug 14, 2018

Let the quantity in volume be "x".
First case revenue=2x*0.60 (orange:water=1:1 and price per cup is 0.60)
Second case revenue=3x*P (orange:water=1:2 and price per cup is "P")
As they have mentioned revenue is same,
2x*0.60=3x*P
P=0.40

Answer (D)

**GMATGuruNY** · Aug 14, 2018

macjas wrote: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

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

cents.

Show Spoiler

D

**avigutman** · Jul 16, 2021

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**naveeng15** · Jan 7, 2022

o 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

**Dereno** · Feb 24 at 03:12am

Let us consider a glass of water = glass of orange juice = x
Initial , one glass of water mixed with one glass of orange juice = x+x = 2x
Price per glass is $0.6
Revenue = 0.6*2x = 1.2x

Now, one glass orange juice mixed with two glasses of water = x+ 2x = 3x
this 3x generates the same revenue of 1.2x
3x * (Rate per glass) = 1.2x
Rate per glass = $ 0.4

**NoraUnoSama** · Feb 25 at 01:25pm

On the first day 0.5 Vol of Orange + 0.5 Vol of Water gave 1 Volume of Orangeade

On the second day 0.5 Vol of Orange + 1 Vol of Water (twice the vol of Orange ) gave 1.5 Vol of Orangeade

Sold at the Same revenue, we have 1* 0.6 = 1.5 x where 0.6 is the price on the first day and x that on the second.

x = 0;6*(1/1.5) = 0.6*(1/1)*(2/3) = 1.2 / 3 = 0.4$ = Answer D.

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