Question: In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?
- 1 : 3
- 1 : 2
- 2 : 3
- 2 : 1
- 3 : 1
Correct Answer: B
Solution and Explanation:
Approach Solution 1:
The problem statement asks to find the ratio of mixing 20% methyl alcohol with 50% methyl alcohol so that the resultant solution holds 40% methyl alcohol.
To find the ratio of two solutions in a resultant mixture, the weighted average works well. We will use this formula:
\((Concen_A)(Vol_A)+(Concen_B)(Vol_B) = (Concen_{A+B})(Vol_{A+B})\)
Let us consider A = volume of the solution with 20 percent alcohol
Let us consider B = volume of the solution with 50 percent alcohol
A + B = resultant mixture
(.20)(A) + (.50)(B) = .40(A + B)
=>(20)(A) + (50)(B) = 40(A + B)
=>20A + 50B = 40A + 40B
=>10B = 20A
The ratio is either A/B or B/A.
Candidates should be careful about the order.
The problem statement asks for the ratio of the 20% solution to the 50% solution
This means it is asking for the ratio of A to B.
10B = 20A
10/20=A/B
A:B = 1:2
Therefore, the ratio of two solutions in a resultant mixture= 1:2.
Approach Solution 2:
As per the problem statement, one solution is 20% and the other is 50%, and the mixture has an average of 40%.
Now having both 20% and 50% being equal, the average would be 20+50/2 =70/2 =35%
However, the average is 40%, which is even further nearer to 50%, hence the quantity of 50% should be more than 20%.
This is considered a weighted average method.
QTY of 20%/QTY of 50% = Distance of average from 50%/ distance of average from 20%
= 50-40/40-20
=½
Hence, the ratio is 1:2
Approach Solution 3:
The problem statement asks to find the ratio of mixing 20% methyl alcohol with 50% methyl alcohol so that the resultant solution holds 40% methyl alcohol.
We can solve the problem by using the allegation method:
20 50
40
10 20
Therefore, the ratio of two solutions in a resultant mixture= 10:20 = 1:2
“In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions allow the candidates to evaluate information and interpret numerical problems. GMAT Quant practice papers help the candidates to practice different types of questions that will improve their mathematical knowledge.
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