A grocer had 1600 kgs of wheat. He sold a part of it at 20% profit and the rest at 12% profit, so that he made a total profit of 17%. How much wheat (in kg) did he sell at 20% profit?

Options

A. 600
B. 1000
C. 800
D. 1200

Answer

To solve the problem step by step, we can use the concept of allegations to find out how much wheat was sold at 20% profit.

### Step 1: Understand the Given Information
- Total wheat = 1600 kg
- Profit on part 1 (sold at 20%) = 20%
- Profit on part 2 (sold at 12%) = 12%
- Overall profit = 17%

### Step 2: Set Up the Allegation
We can use the allegation method to find the ratio of the quantities sold at different profits.

- Profit from part 1 (20%) - Overall profit (17%) = 20% - 17% = 3%
- Overall profit (17%) - Profit from part 2 (12%) = 17% - 12% = 5%

### Step 3: Write the Allegation
The ratio of the quantities sold at 20% profit to the quantities sold at 12% profit can be represented as:
- Quantity at 20% profit : Quantity at 12% profit = 5 : 3

### Step 4: Calculate the Total Parts
The total parts in the ratio = 5 + 3 = 8 parts.

### Step 5: Find the Value of Each Part
Since the total quantity of wheat is 1600 kg, we can find the value of one part:
- Value of one part = Total wheat / Total parts = 1600 kg / 8 = 200 kg

### Step 6: Calculate the Quantity Sold at 20% Profit
Now, we can find the quantity of wheat sold at 20% profit:
- Quantity sold at 20% profit = 5 parts = 5 * 200 kg = 1000 kg

### Final Answer
The grocer sold **1000 kg** of wheat at a 20% profit.

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