In what proportion, must wheat at rs 6.20 per kg be mixed with wheat at rs 7.20 per kg , so that the mixture be worth rs 6.50 per kg ?

Answer

To solve the problem of mixing two types of wheat at different prices to achieve a desired price for the mixture, we can use the method of alligation. Here's a step-by-step solution:

### Step 1: Identify the Prices
We have two types of wheat:
- Wheat A: ₹6.20 per kg
- Wheat B: ₹7.20 per kg
- Desired price of the mixture: ₹6.50 per kg

### Step 2: Set Up the Alligation Formula
We will use the alligation method to find the ratio in which the two types of wheat should be mixed. The formula for alligation is:

\[ \text{Ratio} = \frac{\text{Price of Wheat B} - \text{Price of Mixture}}{\text{Price of Mixture} - \text{Price of Wheat A}} \]

### Step 3: Calculate the Differences
Now, we will calculate the differences:
- Difference between Wheat B and the Mixture:
\[ 7.20 - 6.50 = 0.70 \]
- Difference between the Mixture and Wheat A:
\[ 6.50 - 6.20 = 0.30 \]

### Step 4: Set Up the Ratio
Now, we can set up the ratio using the differences calculated:
\[ \text{Ratio} = \frac{0.70}{0.30} \]

### Step 5: Simplify the Ratio
To simplify the ratio:
\[ \frac{0.70}{0.30} = \frac{7}{3} \]

### Step 6: Conclusion
Thus, the wheat at ₹6.20 per kg must be mixed with wheat at ₹7.20 per kg in the ratio of 7:3.