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A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%. What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
- a)1:3
- b)1:2
- c)2:3
- d)2:1
- e)3:1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A certain quantity of 40% concentration solution is replaced with 25% ...
After the replacement, the concentration of the combined solution becomes 35%. We can use the concept of weighted averages to solve this problem.
The initial solution of 40% concentration is being replaced with a 25% concentration solution. The resulting concentration of the combined solution is 35%. This means that the 40% solution is being diluted.
To find the ratio of the amounts, we can set up the following equation based on the concentrations and quantities:
(40% * x) + (25% * y) = 35% * (x + y)
where "y" represents the amount of the 25% concentration solution that was added.
Simplifying the equation:
(0.4x) + (0.25y) = 0.35x + 0.35y
0.25y - 0.35y = 0.35x - 0.4x
-0.1y = -0.05x
y/x = 0.05/0.1
y/x = 1/2
From the equation, we can see that the ratio of the amount of solution that was replaced (y) to the amount of solution that was not replaced (x) is 1:2.
Therefore, the correct answer is B: 1:2.
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A certain quantity of 40% concentration solution is replaced with 25% ...
Problem:
A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%. What is the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
Solution:
To solve this problem, let's assume that the initial quantity of the 40% concentration solution is 'x' units.
Step 1: Determining the amount replaced:
Let's say 'y' units of the 40% concentration solution is replaced with the 25% concentration solution.
Therefore, the amount of the 40% concentration solution that remains after replacement = x - y.
Step 2: Calculating the concentration of the combined amount:
The concentration of the combined amount is given as 35%.
The concentration of the 40% solution is 40% of x, which is 0.4x.
The concentration of the 25% solution is 25% of y, which is 0.25y.
The concentration of the combined amount can be calculated by finding the average of the concentrations of the two solutions:
(0.4x - 0.4y + 0.25y) / (x - y) = 0.35
Simplifying the equation:
0.4x - 0.4y + 0.25y = 0.35(x - y)
0.4x - 0.4y + 0.25y = 0.35x - 0.35y
0.05x = 0.15y
Dividing both sides of the equation by 0.15:
0.05x / 0.15 = y
Simplifying further:
x / 3 = y
Therefore, the amount of solution that was replaced (y) is equal to one-third of the initial amount of solution (x).
Step 3: Calculating the ratio:
The ratio of the amount of solution that was replaced to the amount of solution that was not replaced can be calculated as follows:
Amount replaced : Amount not replaced
y : (x - y)
Substituting the value of y from Step 2:
x / 3 : (x - x / 3)
x / 3 : 2x / 3
Simplifying the ratio:
1 : 2
Hence, the ratio of the amount of solution that was replaced to the amount of solution that was not replaced is 1:2, which corresponds to option B.
A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%. What is the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
Solution:
To solve this problem, let's assume that the initial quantity of the 40% concentration solution is 'x' units.
Step 1: Determining the amount replaced:
Let's say 'y' units of the 40% concentration solution is replaced with the 25% concentration solution.
Therefore, the amount of the 40% concentration solution that remains after replacement = x - y.
Step 2: Calculating the concentration of the combined amount:
The concentration of the combined amount is given as 35%.
The concentration of the 40% solution is 40% of x, which is 0.4x.
The concentration of the 25% solution is 25% of y, which is 0.25y.
The concentration of the combined amount can be calculated by finding the average of the concentrations of the two solutions:
(0.4x - 0.4y + 0.25y) / (x - y) = 0.35
Simplifying the equation:
0.4x - 0.4y + 0.25y = 0.35(x - y)
0.4x - 0.4y + 0.25y = 0.35x - 0.35y
0.05x = 0.15y
Dividing both sides of the equation by 0.15:
0.05x / 0.15 = y
Simplifying further:
x / 3 = y
Therefore, the amount of solution that was replaced (y) is equal to one-third of the initial amount of solution (x).
Step 3: Calculating the ratio:
The ratio of the amount of solution that was replaced to the amount of solution that was not replaced can be calculated as follows:
Amount replaced : Amount not replaced
y : (x - y)
Substituting the value of y from Step 2:
x / 3 : (x - x / 3)
x / 3 : 2x / 3
Simplifying the ratio:
1 : 2
Hence, the ratio of the amount of solution that was replaced to the amount of solution that was not replaced is 1:2, which corresponds to option B.
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