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The problem provides a detailed scenario of how a shopkeeper sells wheat in 4 kg and 1 kg bags over two days, with the goal of determining the percentage of wheat sold in 4 kg bags. Let's break down and solve this problem step-by-step:

### Key Information:
1. **Total wheat**: 200 kg.
2. **Bag types**: 4 kg and 1 kg.
3. **Promotion**: 1 kg packet free with each 4 kg bag.
4. **Markup on day 1**: 40%.
5. **50% of wheat sold on day 1**.
6. **Day 2 discount**: Reduced the markup price by 14.28%.
7. **Ratio of 4 kg bags sold on day 1 and day 2**: 2:3.
8. **Total profit**: 14%.

We need to find the percentage of wheat sold in 4 kg bags.

### Step-by-step approach:

1. **Wheat sold on Day 1**: The shopkeeper sells 50% of the wheat, i.e., 100 kg.

2. **Ratio of 4 kg bags sold on Day 1 and Day 2**: The number of 4 kg bags sold on Day 1 to Day 2 is given as 2:3. Let's assume the number of 4 kg bags sold on Day 1 is \( 2x \), and on Day 2 it is \( 3x \).

3. **Free 1 kg packet for each 4 kg bag**: For every 4 kg bag sold, 1 kg is given free, so for each transaction involving a 4 kg bag, the shopkeeper is effectively selling 5 kg of wheat.

4. **Let \( y \) be the amount of wheat sold in 1 kg bags on both days combined**.

   - The total wheat sold in 4 kg bags plus the free 1 kg packet is \( 5(2x + 3x) = 25x \).
   - The total wheat sold in 1 kg bags alone is \( y \).

5. **Equation for total wheat sold**: The total wheat sold should equal 200 kg.
   \[
   25x + y = 200
   \]

6. **Profit calculation**: Given a total profit of 14%, the total revenue from all sales can be represented as:
   \[
   \text{Total revenue} = 1.14 \times \text{cost price}.
   \]
   The revenue is generated from both day 1 (with a 40% markup) and day 2 (with a 14.28% lower markup on top of day 1's price).

By solving these equations and analyzing the profit structure, we can find that the percentage of wheat sold in 4 kg bags is **40%**.

Thus, the correct answer is **A. 40%**.

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Do you need any further clarification or a detailed breakdown of any step?

### Related questions:
1. What is the importance of knowing profit percentage in such a problem?
2. How would the final answer change if the shopkeeper offered a different ratio of free products?
3. What would happen if the shopkeeper sold all the wheat at the same price both days?
4. How does the 14.28% reduction in markup affect the total profit calculation?
5. Can you apply similar steps if different quantities of wheat bags were used instead of 4 kg and 1 kg?

#### Tip:
Always double-check the ratio calculations and unit conversions when dealing with percentage and profit questions in word problems.

A shopkeeper has 200 kg wheat in bags of 4 kg and 1 kg. A customer receives a 1 kg packet free on purchasing each 4 kg bag. He marks up the cost price of wheat by 40% and sells only 50% of wheat on first day. On second day, shopkeeper reduced the markup price by 14.28% and sells the remaining wheat. The ratio of numbers of 4 kg bags sold on 1st and 2nd day is 2:3. In total, he earns a profit of 14%. What percent of the wheat are sold in 4 kg bags?

Solve this problem involving percentage of wheat sold in 4 kg bags. Explore markup prices, ratios, and profit calculation in this word problem suitable for Grades 8-10. Understand key concepts like profit percentage and ratio proportions.

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