. In what ratio salt costing Rs 13/kg mixed with another salt costing Rs 7/ kg to get a mixture costing Rs 9/kg?

Options

A. `4 : 7`
B. `3 : 5`
C. `2 : 3`
D. `1 : 2`

Answer

To solve the problem of mixing two types of salt to achieve a desired cost per kg, we can use the concept of alligation. Here’s the step-by-step solution:

### Step 1: Identify the costs
Let:
- Cost of Salt 1 (CP1) = Rs 13/kg
- Cost of Salt 2 (CP2) = Rs 7/kg
- Cost of the mixture (CPm) = Rs 9/kg

### Step 2: Calculate the differences
Using the alligation method, we calculate the differences between the costs:
- Difference between CP1 and CPm:
\[ CP1 - CPm = 13 - 9 = 4 \]
- Difference between CP2 and CPm:
\[ CPm - CP2 = 9 - 7 = 2 \]

### Step 3: Set up the ratio
The ratio of the quantities of the two salts is given by the differences calculated:
- Ratio of Salt 1 to Salt 2:
\[ \text{Ratio} = \frac{4}{2} = 2:1 \]

### Step 4: Conclusion
Thus, the ratio in which the two salts should be mixed is **2:1**.