Box A contains wheat worth `₹ 30` per kg and box B contains wheat worth `₹40 ` per kg. if both A and B are mixed in the ratio `4:7` thent he price of mixture per kg is

Options

A. `36.36
B. `35.80`
C. `42.50`
D. `31.30`

Explanation

To find the price of the mixture per kg when box A and box B are mixed in the ratio of 4:7, we can use the method of alligation. Here’s the step-by-step solution:

### Step 1: Identify the values
- Price of wheat in Box A = ₹30 per kg
- Price of wheat in Box B = ₹40 per kg
- Ratio of mixing = 4:7

### Step 2: Set up the alligation formula
Let the price of the mixture be \( x \). According to the alligation method, we can set up the following relationships:
- The difference between the price of Box B and the price of the mixture: \( 40 - x \)
- The difference between the price of Box A and the price of the mixture: \( x - 30 \)

### Step 3: Set up the ratio using alligation
According to the ratio of mixing (4:7), we can write:
\[ \frac{40 - x}{x - 30} = \frac{4}{7} \]

### Step 4: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 7(40 - x) = 4(x - 30) \]

### Step 5: Expand and simplify the equation
Expanding both sides:
\[ 280 - 7x = 4x - 120 \]

### Step 6: Rearrange the equation
Rearranging gives:
\[ 280 + 120 = 4x + 7x \]
\[ 400 = 11x \]

### Step 7: Solve for \( x \)
Dividing both sides by 11:
\[ x = \frac{400}{11} \approx 36.36 \]

### Conclusion
The price of the mixture per kg is approximately ₹36.36.

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