Solution A contains 10% acid and solution B contains 30% acid. In what ratio should solution A be mixed with Solution B to obtain a mixture with 25% acid?

Options

A. `1:2`
B. `3:1`
C. `1:3`
D. `2:1`

Answer

To solve the problem of mixing Solution A and Solution B to obtain a mixture with 25% acid, we can use the method of alligation. Here’s a step-by-step solution:

### Step 1: Identify the concentrations
- Concentration of Solution A (C1) = 10% acid
- Concentration of Solution B (C2) = 30% acid
- Desired concentration in the mixture (C) = 25% acid

### Step 2: Set up the alligation
We will use the alligation method to find the ratio in which the two solutions should be mixed. The formula for alligation is as follows:

\[ \text{Ratio} = \frac{C2 - C}{C - C1} \]

### Step 3: Calculate the differences
- Difference between concentration of Solution B and the desired concentration:
\[ C2 - C = 30\% - 25\% = 5\% \]
- Difference between the desired concentration and concentration of Solution A:
\[ C - C1 = 25\% - 10\% = 15\% \]

### Step 4: Set up the ratio
Now, substituting the differences into the ratio formula:
\[ \text{Ratio} = \frac{5\%}{15\%} = \frac{1}{3} \]

### Step 5: Conclusion
Thus, the ratio in which Solution A should be mixed with Solution B to obtain a mixture with 25% acid is **1:3**.

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