A mixture worth Rs 3.25 per kg is formed by mixing two types of salts, one costing Rs 3.10 per kg while the other Rs 3.60 per kg. In what ratio must they have been mixed?

Answer

To solve the problem of mixing two types of salts to achieve a desired price per kg using the method of alligation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Prices**:
- Let the price of the first salt (A) be Rs 3.10 per kg.
- Let the price of the second salt (B) be Rs 3.60 per kg.
- The price of the mixture (M) is Rs 3.25 per kg.

2. **Set Up the Alligation Formula**:
- We will use the alligation method to find the ratio in which the two salts should be mixed.
- The formula for alligation is:
\[ \text{Difference from A} = M - A \]
\[ \text{Difference from B} = B - M \]

3. **Calculate the Differences**:
- Calculate the difference between the mixture price and the price of the first salt:
\[ \text{Difference from A} = 3.25 - 3.10 = 0.15 \]
- Calculate the difference between the price of the second salt and the mixture price:
\[ \text{Difference from B} = 3.60 - 3.25 = 0.35 \]

4. **Set Up the Ratio**:
- The ratio of the two salts is given by the inverse of the differences calculated:
\[ \text{Ratio of A to B} = \frac{\text{Difference from B}}{\text{Difference from A}} = \frac{0.35}{0.15} \]

5. **Simplify the Ratio**:
- To simplify the ratio, we can divide both sides by 0.05:
\[ \frac{0.35 \div 0.05}{0.15 \div 0.05} = \frac{7}{3} \]
- Therefore, the ratio of salt A to salt B is 7:3.

### Final Answer:
The two types of salts must be mixed in the ratio of **7:3**.

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