Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. What part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
- 1/5
- 2/7
- 7/11
- 6/7
- 7/8
Correct Answer: C
Solution and Explanation
Approach Solution 1:
Given:
- A vessel is filled with liquid
- 3 parts of which are water
- 5 parts of it is syrup.
Find out:
- What part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
As per the problem statement, the quantity of water and syrup are:
Water = 3/8
Syrup = 5/8
Let x part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup
After:
Water = 3/8(1-x) + x
Syrup = 5/8(1-x)
Now, since mixture becomes half water and half syrup, we get:
3/8(1-x) + x = 5/8(1-x)
2/8(1-x) = x
(1-x) = 4x
x = ⅕
Hence, the correct answer is A.
Approach Solution 2:
Given:
- A vessel is filled with liquid
- 3 parts of which are water
- 5 parts of it is syrup.
Find out:
- What part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Final/Initial =\((1−b/a)^n\)
Final = The Final Quantity of that component who's concentration is being reduced.
Initial = The Initial Quantity of that component who's concentration is being reduced.
Let us consider:
b = Amount of liquid replaced
a = Final Volume in the container after the replacement of quantity b.
n = number of times the operation is done
Here the concentration of syrup is being reduced.
Initial quantity = 5/8 Final quantity = 1/2 (Since the final ratio is 1 : 1)
Therefore,
(½)/ (⅝ ) = 1-b/a
⅘ = 1-b/a
b/a = 1-⅘
b/a = ⅕
Hence, A is the correct answer.
Approach Solution 3:
Let initially vessel have 8 litres of liquid and x litres of this liquid be replaced with water.
Then quantity of water in new mixture = 3-3x/8+8
Quantity of syrup in new mixture= 5-5x/8
ATQ,
After replacement, the quantity water and syrup same
(3-3x/8+x)= (5-5x/8)
==> -3x/8+x+5x/8= 5-3
==> (-3x+8x+5x)/8= 2
==> 10x/8= 2
==>x= 8/5
So, part of the mixture replaced
8/5*1/8
==> 1/5
“A vessel is filled with liquid, 3 parts of which are water and 5 parts”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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