A shopkeeper bought 1000 kg of rice, a part of which was sold at 10% profit and the remaining at 20% loss on the whole the loss was 5% what is the quantity of rice was sold at 20% loss ?

Options

A. 500 kg
B. 600 kg
C. 400 kg
D. 550 kg

Answer

To solve the problem step by step, we can use the concept of allegation to find the quantity of rice sold at a 20% loss.

### Step 1: Understand the Problem
The shopkeeper bought 1000 kg of rice. A portion of this rice was sold at a 10% profit, and the remaining portion was sold at a 20% loss. The overall loss on the entire quantity of rice was 5%. We need to find out how much rice was sold at a 20% loss.

**Hint:** Start by identifying the total quantity and the profit/loss percentages involved.

### Step 2: Set Up the Allegation
We will use the allegation method to relate the profit and loss percentages.

- Profit percentage = 10%
- Loss percentage = 20%
- Overall loss percentage = 5%

**Hint:** Use the formula for allegation, which is to subtract the overall percentage from the profit and loss percentages.

### Step 3: Calculate the Differences
Using the allegation method:
- Difference between profit and overall loss = 10% - (-5%) = 10% + 5% = 15%
- Difference between overall loss and loss percentage = -5% - 20% = -5% + 20% = 15%

**Hint:** The differences calculated will help us find the ratio of quantities sold at profit and loss.

### Step 4: Set Up the Ratio
From the differences calculated, we can set up the ratio:
- Ratio of quantity sold at profit (10%) to quantity sold at loss (20%) = 15:15 = 1:1

**Hint:** This means that for every kg sold at a profit, an equal kg was sold at a loss.

### Step 5: Calculate the Quantities
Let the quantity sold at a profit be x kg and the quantity sold at a loss be x kg. Since the total quantity is 1000 kg:
- x + x = 1000 kg
- 2x = 1000 kg
- x = 500 kg

**Hint:** Since x represents both quantities, you can conclude that both sold quantities are equal.

### Step 6: Find the Quantity Sold at 20% Loss
Since we have found that x = 500 kg:
- Quantity sold at 20% loss = 500 kg

**Hint:** This is the final answer to the question.

### Final Answer
The quantity of rice sold at a 20% loss is **500 kg**.