To solve the problem using the alligation method, we first need to set up the information we have:
- Concentration of the desired solution: 12%
- Concentration of the first solution (15%): Higher concentration
- Concentration of the second solution (3%): Lower concentration
Next, we calculate the differences:
-
Difference between the concentration of the first solution (15%) and the desired concentration (12%): \[ 15% - 12% = 3% \]
-
Difference between the concentration of the second solution (3%) and the desired concentration (12%): \[ 12% - 3% = 9% \]
Now, we can create a proportion based on these differences. According to the alligation method, the ratio of the two solutions can be found as follows:
- The ratio of 15% solution to the 3% solution: \[ \text{Ratio} = \frac{9}{3} = 3:1 \]
This means that for every 3 parts of the 15% solution, there is 1 part of the 3% solution.
Now, let’s determine the total parts of the mixture:
- Total parts = 3 parts (15% solution) + 1 part (3% solution) = 4 parts
We are told we have 480ml of the 3% solution, which corresponds to 1 part in the ratio. To find the volume of one part, we can calculate:
\[ \text{Volume of one part} = \frac{480 \text{ ml}}{1} = 480 \text{ ml} \]
Now, we can find the volume of the 15% solution, which corresponds to 3 parts:
\[ \text{Volume of 15% solution} = 3 \times 480 \text{ ml} = 1440 \text{ ml} \]
Thus, the amount of 15% solution needed to prepare 12% solution using 480 ml of 3% stock solution is 1440 ml.