One quality of wheat at Rs. 9.30 per kg is mixed with another quality at a certain rate in the ratio 8:7. If the mixture so formed be worth Rs. 10 per kg, what is the rate per kg of the second quality of wheat ?

Options

A. Rs. 10.30
B. Rs. 10.60
C. Rs. 10.80
D. Rs. 11

Answer

To find the rate per kg of the second quality of wheat, we can use the concept of alligation. Here’s a step-by-step solution:

### Step 1: Identify the known values
- Price of the first quality of wheat (A) = Rs. 9.30 per kg
- Price of the mixture (M) = Rs. 10 per kg
- Ratio of the two qualities of wheat = 8:7

### Step 2: Set up the alligation
Let the price of the second quality of wheat (B) be Rs. x per kg. We can set up the alligation as follows:

\[ \text{Price of A} \quad \text{Price of M} \quad \text{Price of B} \]
\[ 9.30 \quad \quad 10 \quad \quad x \]

### Step 3: Calculate the differences
Using the alligation method, we calculate the differences:

- Difference between the price of A and the price of M:
\[ 10 - 9.30 = 0.70 \]

- Difference between the price of M and the price of B:
\[ x - 10 \]

### Step 4: Set up the ratio
According to the ratio of the two qualities (8:7), we can set up the equation:
\[ \frac{0.70}{x - 10} = \frac{8}{7} \]

### Step 5: Cross-multiply to solve for x
Cross-multiplying gives us:
\[ 0.70 \cdot 7 = 8 \cdot (x - 10) \]
\[ 4.90 = 8x - 80 \]

### Step 6: Rearrange the equation
Rearranging the equation to isolate x:
\[ 8x = 4.90 + 80 \]
\[ 8x = 84.90 \]

### Step 7: Solve for x
Now, divide both sides by 8:
\[ x = \frac{84.90}{8} = 10.6125 \]

### Step 8: Final answer
Thus, the rate per kg of the second quality of wheat is approximately Rs. 10.61.

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