In what ratio must a mixture of 15% spirit strength be mixed with that of 25% spirit strength to get a mixture of 21% spirit strength?

Options

A. `1:3`
B. `2:3`
C. `3:4`
D. `4:5`

Answer

To solve the problem of mixing two solutions of different spirit strengths to achieve a desired concentration, we can use the method of alligation. Here's a step-by-step solution:

### Step 1: Identify the given percentages
We have:
- Mixture A: 15% spirit strength
- Mixture B: 25% spirit strength
- Desired mixture: 21% spirit strength

### Step 2: Set up the alligation formula
In alligation, we find the differences between the strengths of the mixtures and the desired strength.

### Step 3: Calculate the differences
- Difference between Mixture A and Desired Mixture:
\[ 21\% - 15\% = 6\% \]

- Difference between Mixture B and Desired Mixture:
\[ 25\% - 21\% = 4\% \]

### Step 4: Write the ratio
Now, we can express the ratio of the two mixtures using the differences calculated:
\[ \text{Ratio} = \frac{\text{Difference of B and X}}{\text{Difference of A and X}} = \frac{4}{6} \]

### Step 5: Simplify the ratio
To simplify the ratio \( \frac{4}{6} \):
\[ \frac{4}{6} = \frac{2}{3} \]

### Conclusion
Thus, the required ratio in which the mixture of 15% spirit strength must be mixed with that of 25% spirit strength to get a mixture of 21% spirit strength is:
\[ \text{Ratio} = 2 : 3 \]