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 amout 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?
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srcc25anu
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Let quantity of orage juice on Day 1 be X Lts
Let quantity of water on Day 1 be Y Lts
Total Orangeade = X + Y Lts
Let quantity in each glass be N lts
# of glasses sold = x+y / n
SOld at 0.6 per glass
Total revenue on Day 1 = 0.6 * (X+Y) / n
Next DAy,
he mixed 2x orange juice + Y water to obtain 2X+Y orangeade. Again if each glass quantity is N lts, # of glasses on Day 2 = (2X+Y)/N. Also stated he made same revenue on Day 2 as day 1. Thus price per glass on Day 2 can be calculated as: [0.6 * (X+Y) / n] / [(2X+Y)/N ]
Let quantity of water on Day 1 be Y Lts
Total Orangeade = X + Y Lts
Let quantity in each glass be N lts
# of glasses sold = x+y / n
SOld at 0.6 per glass
Total revenue on Day 1 = 0.6 * (X+Y) / n
Next DAy,
he mixed 2x orange juice + Y water to obtain 2X+Y orangeade. Again if each glass quantity is N lts, # of glasses on Day 2 = (2X+Y)/N. Also stated he made same revenue on Day 2 as day 1. Thus price per glass on Day 2 can be calculated as: [0.6 * (X+Y) / n] / [(2X+Y)/N ]
Hi thanks for your response:
I dont think the working you have done is correct.
He keeps the orange juice content the same but increases the water?
I am not sure how it is solved usig your method. You would end up with .6 (1/2)?
Which would equal .3???
I dont think the working you have done is correct.
He keeps the orange juice content the same but increases the water?
I am not sure how it is solved usig your method. You would end up with .6 (1/2)?
Which would equal .3???
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Anju@Gurome
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On the 1st day, 1 unit of orange juice was mixed with 1 unit of water.cpay3245 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 amout 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?
So, total amount of orangeade = (1 + 1) = 2 units
If each glass contained n units of orangeade, total number of glasses sold = 2/n
As price per glass was $0.60, total revenue on the 1st day = (0.60)*(2/n)
On the 1st day, 1 unit of orange juice was mixed with 2 units of water.
So, total amount of orangeade = (1 + 2) = 3 units
If each glass contained n units of orangeade, total number of glasses sold = 3/n
Total revenue on the 2nd day = Total revenue on the 1st day = (0.60)*(2/n)
Hence, price per glass on the 2nd day = (Total revenue)/(number of glasses sold) = (0.60)*(2/n)/(3/n) = (0.60)*(2/n)*(n/3) = (0.20)*2 = 0.40
The correct answer is D.
Note : Just put X = Y in the equation derived by srcc25anu as on the first day amount of orange juice is equal to amount of water.
Anju Agarwal
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sonalibhangay
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Let us for example take that on
First Day : No. of Glasses made = 10 (5 Juice + 5 Water) Price : $0.6 Revenue :$0.6*10 = $6
Second Day :No. of Glasses made = 15 (5 Juice + 10 Water) Price : $x Revenue :15*x = $6
Therefore Equation Becomes $6 / 15 = x and x is [spoiler]$ 0.4 (Ans D)[/spoiler]
First Day : No. of Glasses made = 10 (5 Juice + 5 Water) Price : $0.6 Revenue :$0.6*10 = $6
Second Day :No. of Glasses made = 15 (5 Juice + 10 Water) Price : $x Revenue :15*x = $6
Therefore Equation Becomes $6 / 15 = x and x is [spoiler]$ 0.4 (Ans D)[/spoiler]
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GMATGuruNY
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Let each glass = 1 unit.On a certain day, orangeade was made by mixing a certain amount of 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
First day:
Let water = 1 unit and juice = 1 unit.
Glasses = water + juice = 1+1 = 2.
Since each glass earns 60 cents, revenue = 2*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.
The correct answer is D.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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