Two solutions of milk and water are mixed in the ratio 2: 3 by volume. The resulting solution contains 40 % milk. Find milk concentration in the first solution if the concentration of milk in the second is 60%a.20 %b.40 %c.10 %d.30 %
Question
Two solutions of milk and water are mixed in the ratio 2: 3 by volume. The resulting solution contains 40 % milk. Find milk concentration in the first solution if the concentration of milk in the second is 60%a.20 %b.40 %c.10 %d.30 %
Solution
Let's denote the concentration of milk in the first solution as x (in percentage).
We know that the two solutions are mixed in the ratio 2:3. This means that for every 2 parts of the first solution, we have 3 parts of the second solution.
We also know that the resulting solution contains 40% milk. This can be expressed as a weighted average of the milk concentrations in the first and second solutions, with the weights corresponding to the volumes of the solutions.
So, we can set up the following equation:
2/5 * x + 3/5 * 60 = 40
This equation represents the fact that the overall concentration of milk is a weighted average of the concentrations in the individual solutions, with the weights given by the volumes of the solutions.
Solving this equation for x gives:
2x + 180 = 200
2x = 200 - 180
2x = 20
x = 20 / 2
x = 10
So, the concentration of milk in the first solution is 10%, which corresponds to option c.
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