In what proportion must wheat at Rs. 1.60 per kg be mixed with wheat at Rs.1.45 per kg. So that the mixture be worth Rs. 1.54 per kg ?

Options

A. 2 : 3
B. 3 : 2
C. 3 : 4
D. 4 : 3

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
Let:
- Price of Wheat 1 (W1) = Rs. 1.60 per kg
- Price of Wheat 2 (W2) = Rs. 1.45 per kg
- Price of the mixture (M) = Rs. 1.54 per kg

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

### Step 3: Calculate the Differences
Using the alligation formula, we calculate the differences:
- Difference between W1 and M:
\( W1 - M = 1.60 - 1.54 = 0.06 \)
- Difference between W2 and M:
\( M - W2 = 1.54 - 1.45 = 0.09 \)

### Step 4: Write the Alligation
Now, we can set up the alligation as follows:

```
W1 (1.60)
|
| 0.06
|
M (1.54)
|
| 0.09
|
W2 (1.45)
```

### Step 5: Determine the Ratio
The ratio of the quantities of Wheat 1 and Wheat 2 is inversely proportional to the differences calculated:
- Ratio of Wheat 1 to Wheat 2 = Difference of W2 and M : Difference of W1 and M
- Thus, the ratio is \( 0.09 : 0.06 \)

### Step 6: Simplify the Ratio
To simplify the ratio:
- Convert the differences to whole numbers:
\( 0.09 : 0.06 = 9 : 6 \)
- This can be simplified further:
\( 9 : 6 = 3 : 2 \)

### Final Answer
The required proportion in which Wheat at Rs. 1.60 per kg must be mixed with Wheat at Rs. 1.45 per kg is **3:2**.

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