Question: How many litres of a 90% solution of concentrated acid needs to be mixed with a 75% solution of concentrated acid to get a 30 L solution of 78% concentrated acid?
- 24 L
- 22.5 L
- 6 L
- 17.5 L
- 25 L
“How Many Litres of a 90% Solution of Concentrated Acid Needs to be Mixed with a 75% Solution GMAT Problem Solving” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation
There is only one way to solve the problem.
Approach Solution:
Explanation: For the following problem, calculate the volume of a mixture of concentrated acids. You will be given the total mixture volume and need to calculate how many litres of each acid solution you need. Lets evaluate the problem further
Let A be the amount of solution of concentrated acid which is 90%
Let B be the amount of solution of concentrated acid which is 75%
Since total volume given is 30 L,
equation 1 will become,
A + B = 30
Amount of acid in A L of 90% concentrated acid = \(A*\frac{90}{100} \) = 0.9 A
Amount of acid in B L of 75% concentrated acid = \(A*\frac{75}{100} \) = 0.75 B
Amount of acid in 30 L of 90% concentrated acid =\(A*\frac{78}{100} \)= 23.4
Equation 2 will become,
0.9 A + 0.75 B = 23.4
By multiplying equation 1 by 0.9 we will get equation 3
Equation 3 will become,
0.9 A + 0.9 B = 27
Now on Subtracting equation 2 from 3
We get 0.15 B = 3.6
Value of B will be
B =\(\frac{3.60}{0.15} \) = 24
Now, From equation 1
A + B = 30
A = 30 - B
A = 30 - 24
A = 6
Therefore, 6 ltr of 90% solution of concentrated acid has to be mixed with 75% solution of concentrated acid to get 30 ltr solution of 78% concentrated acid.
Answer is C, which is 6 litres
Answer: C
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