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08 Jul 2021, 06:30
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Difficulty:
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87% (01:53) correct
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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
A. 1,800 mL
B. 1,900 mL
C. 2,000 mL
D. 2,100 mL
E. 2,200 mL
08 Jul 2021, 06:39
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Bunuel
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
08 Jul 2021, 13:37
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Bunuel
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!
