Question: How many litres of pure alcohol must be added to a 100-litre solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?
- 7/2
- 5
- 20/3
- 8
- 39/4
“How many litres of pure alcohol must be added to a 100-litre solution that is 20 percent alcohol”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
The given condition states that there is a 100 litre solution in which 20% alcohol is present. We need to find the litres of pure alcohol that can be added in the 100 litre solution so as to produce the solution which has 25% of alcohol.
20% Alcohol solution means that, in the 100 litre solution there is 20 litres of solution which is alcohol and 80 litres other solvents.
If we add "x" litres of alcohol to the solution, the solution becomes "100+x" litres and alcohol, which was 20 litres, becomes 20+x litres.
According to the statement;
20+x = 25% of (100+x)
OR
20+x=(100+x)/4
80+4x=100+x
3x=20
x=20/3
Correct Answer: C
Approach Solution 2:
Based on the given condition, it is identified that there is a 100 litre solution in which 20% alcohol is present. We need to find the litres of pure alcohol that can be added in the 100 litre solution so as to produce the solution which has 25% of alcohol.
20% * 100 litres = 20 litres
Accordingly, by adding alcohol to the solution, the volume would be altered, so it's no longer going to be just 100 litres. This implies 100 + x litres of solution after adding more alcohol.
In addition, when more alcohol is added, there is not just 20 litres of alcohol, there is going to be 20 + x litres of alcohol.
We need to find - how much alcohol must be added to result in there being 25% alcohol.
This implies that-
20% * 100 = 20 litres
But, now we have:
25% * (100 + x) = (20 + x)
Now, let's just solve for x:
Converting the percentage and multiplying:
25/100 * (100 + x) = 20 + x
2500 + 25x/ 100 = 20 + x
Simplifying the left side, we get:
25(100 + x)/100 = 20 + x
Cancelling out items, we get
100 + x/ 4 = 20 + x
Multiplying both sides by 4, we get:
4(100 + x/4) = 4(20 +x)
100 + x = 80 + 4x
Subtracting x from left side:
100 = 80 + 3x
Subtracting 80 from right side we get:
20 = 3x
Dividing we get:
X = 20/3
Correct Answer: C
Approach Solution 3:
According to the situation, there is a 100-liter solution containing 20% alcohol. To create a solution with 25% alcohol, we must determine how many litres of pure alcohol may be added to a 100-liter solution.
According to the definition of a 20% alcohol solution, there are 80 litres of other solvents and 20 litres of alcohol in a 100 litre solution.
If we add "x" litres of alcohol to the solution, the alcohol, which was 20 litres, becomes 20+x litres and the solution becomes "100+x" litres.
based on the assertion;
20+x = 25% of (100+x)
OR
20+x=(100+x)/4
80+4x=100+x
3x=20
x=20/3
Correct Answer: C
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