The problem involves finding the ratio of two quantities based on the concept of weighted average. Let us break it down step by step.

Given:

1. Cost of the first type of wheat = ₹25 per kg.
2. Cost of the second type of wheat = ₹30 per kg.
3. Cost of the mixture = ₹28 per kg.

We need to find the ratio of the quantities of the two types of wheat.

Solution:

We use the rule of alligation, which states:

$\text{Ratio of quantities} = \frac{\text{Difference between the cost of the second type and the mixture}}{\text{Difference between the cost of the first type and the mixture}}.$

Step-by-step:

1. Difference between the cost of the second type and the mixture: $30 - 28 = 2$

2. Difference between the cost of the first type and the mixture: $28 - 25 = 3$

3. Ratio of the two types: $\text{Ratio} = \frac{2}{3}$

Thus, the ratio of the quantities of the two types of wheat is $2:3$.

Final Answer:

Option (3): 2:3

Do you want further details on the explanation or have any other questions?

Related Questions:

1. What is the rule of alligation and its applications in other problems?
2. How would the solution change if the cost of the mixture were different?
3. Can this problem be solved using a different mathematical method?
4. How does this concept apply to real-world mixing problems, such as in chemistry or finance?
5. What would the ratio be if the prices of the two wheat types were the same?

Tip:

The rule of alligation is a quick way to solve problems involving mixtures, but always double-check by verifying if the weighted average calculation holds true!