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A mixture contains nothing but water and acetone in a ratio of 1 : 2.

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Bunuel
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A mixture contains nothing but water and acetone in a ratio of 1 : 2. [#permalink] New post   08 Jul 2021, 06:30
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A mixture contains nothing but water and acetone in a ratio of 1 : 2. After 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3. What is the original volume of the mixture ?

A. 1,800 mL
B. 1,900 mL
C. 2,000 mL
D. 2,100 mL
E. 2,200 mL
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BrentGMATPrepNow
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A mixture contains nothing but water and acetone in a ratio of 1 : 2. [#permalink] New post   08 Jul 2021, 06:39
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Bunuel wrote:
A mixture contains nothing but water and acetone in a ratio of 1 : 2. After 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3. What is the original volume of the mixture ?

A. 1,800 mL
B. 1,900 mL
C. 2,000 mL
D. 2,100 mL
E. 2,200 mL


Let W = the ORIGINAL volume of water in the mixture
Let A = the ORIGINAL volume of acetone in the mixture

A mixture contains nothing but water and acetone in a ratio of 1 : 2
We can write: W/A = 1/2
Cross multiply to get: 2W = A

After 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3.
So, W + 200 = the volume of water in the NEW mixture
And A = the volume of acetone in the NEW mixture
So we can write: (W + 200)/A = 2/3
Cross multiply: 3(W + 200) = 2A
Expand: 3W + 600 = 2A

We now have the following system of equations:
2W = A
3W + 600 = 2A

Take the top equation and multiply both sides by 2 to get:
4W = 2A
3W + 600 = 2A

Since both equations are set equal to 2A, they must be equal: 4W = 3W + 600
Solve: W = 600

Since W = 600, and since we already know 2W = A, we can conclude that A = 1200

What is the original volume of the mixture ?
Original volume = W + A
= 600 + 1200 = 1800

Answer: A
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Re: A mixture contains nothing but water and acetone in a ratio of 1 : 2. [#permalink] New post   08 Jul 2021, 13:37
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Bunuel wrote:
A mixture contains nothing but water and acetone in a ratio of 1 : 2. After 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3. What is the original volume of the mixture ?

A. 1,800 mL
B. 1,900 mL
C. 2,000 mL
D. 2,100 mL
E. 2,200 mL


Let the amount of water be x
Acetone = 2x
200ml of water is added, which means no change in amount of acetone:
\(\frac{x + 200}{2x }= \frac{2}{3}\)
3x + 600 = 4x
x = 600 - Volume of water
Volume of Acetone = 2x = 1200
Total volume = 1200 + 600 = 1800 - (A), IMO!
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A mixture contains nothing but water and acetone in a ratio of 1 : 2. [#permalink] New post   28 Sep 2022, 05:41
Bunuel wrote:
A mixture contains nothing but water and acetone in a ratio of 1 : 2. After 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3. What is the original volume of the mixture ?

A. 1,800 mL
B. 1,900 mL
C. 2,000 mL
D. 2,100 mL
E. 2,200 mL



The volume of water and acetone in the original mixture can be written as:
Water = 1x mL
Acetone = 2x mL

Since 200mL water is added to the mixture giving the new ratio as 2:3
\((1x+200)/2x=2/3\)
\(3x+600=4x\)
\(x=600\)

Original Mixture = 3x = 3*600 = 1800mL

Hence, answer is option A.
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Re: A mixture contains nothing but water and acetone in a ratio of 1 : 2. [#permalink] New post   13 May 2024, 04:58
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Re: A mixture contains nothing but water and acetone in a ratio of 1 : 2. [#permalink]
13 May 2024, 04:58
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