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

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 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.

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

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.

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

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

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

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.

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)

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)

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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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

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".

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

Video solution from Quant Reasoning starts at 0:27
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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

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.