Question: Two solutions of 90% and 97% purity are mixed resulting in 21 litres of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?
- 15 litres
- 12 litres
- 9 litres
- 6 litres
- 4 litres
Correct Answer: C
Solution and Explanation
Approach Solution 1
This model answer has only 1 approach to solve the problem
The given condition of the problem states that there are two solutions which have been mixed together forming a mixture of 21 litres of solution and is 94% pure. Accordingly, the two solutions have a purity of 90% and 97%. The requirement is to find the quantity of the first solution which consists of 90% purity of the solution. This can be done based on a specific method.
Considering the method of allegation for this problem to be resolved as mentioned below, the following answer has been presented with proper evaluation.
Making use of this method would evaluate the strongest way to solve the problem. Hence, the method can be evaluated as follows:
Let, the quantity of the solution with 90% solution be A
Let, the quantity of the solution with 97% pure solution be B
Accordingly, the total Solution be A+B = 21
This has been given in the condition as well.
The equation is formed as mentioned below:
Concentrate of A + Concentrate of B = Concentrate of (A+B)
This can be clearly evaluated with the values as follows:
90/100 A + 97/100B = 94/100* (A + B)
Solving the entire equation, it can be evaluated that
= 4A = 3B
= A + B = 21, which is a given condition
= A + 4A/3 = 21
= A = 9
Hence, the quantity of the first solution in the resulting mixture is 9 litres which is option C for this problem.
“Two solutions of 90% and 97% purity are mixed resulting in 21 litres”- 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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