In what proportion must a grocer mix wheat at rs `2.04` per kg and rs `2.88` per kg so as to make a mixture of worth rs`2.52` per kg?

Options

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

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 concept of alligation. Here’s a step-by-step solution:

### Step 1: Identify the Prices
We have:
- Price of wheat A (cheaper): Rs 2.04 per kg
- Price of wheat B (costlier): Rs 2.88 per kg
- Price of the mixture: Rs 2.52 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.

1. Calculate the difference between the price of wheat A and the price of the mixture:
\[ \text{Difference A} = \text{Price of A} - \text{Price of mixture} = 2.04 - 2.52 = -0.48 \]
(Since we are looking for a positive difference, we take the absolute value)
\[ \text{Difference A} = 0.48 \]

2. Calculate the difference between the price of wheat B and the price of the mixture:
\[ \text{Difference B} = \text{Price of mixture} - \text{Price of B} = 2.52 - 2.88 = -0.36 \]
(Again, we take the absolute value)
\[ \text{Difference B} = 0.36 \]

### Step 3: Calculate the Ratio
Now, we can find the ratio of the two types of wheat using the differences calculated:
\[ \text{Ratio} = \frac{\text{Difference B}}{\text{Difference A}} = \frac{0.48}{0.36} \]

To simplify:
\[ \text{Ratio} = \frac{48}{36} = \frac{4}{3} \]

### Step 4: Conclusion
The grocer must mix the wheat at Rs 2.04 per kg and Rs 2.88 per kg in the ratio of 4:3.