Question

In what proportions should you mix 7% and 1% solutions to get 4% solution?

Use the alligation method to solve this problem. Provide your answer in x:y format

Answer 1

To solve the problem using the alligation method, we can apply the following steps:

1. Identify the concentrations of the solutions we have and the target concentration. We have:
- Higher concentration = 7%
- Lower concentration = 1%
- Desired concentration = 4%

2. Set up the alligation method by placing the concentrations in the following format:

```
Higher Concentration Desired Concentration
[7%] [4%]

[4%]

Lower Concentration
[1%]
```

3. Calculate the differences:
- Difference between the higher concentration (7%) and the desired concentration (4%):
\[
7\% - 4\% = 3\%
\]

- Difference between the desired concentration (4%) and the lower concentration (1%):
\[
4\% - 1\% = 3\%
\]

4. We can now express the ratio of the two solutions. The proportions of 7% and 1% solutions are found by taking the differences:
- The part of the 1% solution needed is equal to the difference from 7% (3%).
- The part of the 7% solution needed is equal to the difference from 1% (3%).

5. Therefore, the ratio of the two solutions is:
\[
\text{Ratio} = \text{part of 1% solution} : \text{part of 7% solution} = 3 : 3
\]

This simplifies to:
\[
1 : 1
\]

Thus, to obtain a 4% solution, you should mix the 7% and 1% solutions in the ratio **1:1**.