A trader has 50 kg of rice, a part of which he sells at 14% profit and the rest at 6% loss. On the whole his loss is 4%. What is the quantity sold at 14% profit and that at 6% loss?

Options

A. 2,48
B. 4,46
C. 5,45
D. 60,20

Answer

To solve the problem step by step, we will use the allegation method.

### Step 1: Understand the given data
The trader has a total of 50 kg of rice. A part of this rice is sold at a 14% profit, and the remaining part is sold at a 6% loss. The overall loss incurred by the trader is 4%.

### Step 2: Set up the profit and loss percentages
- Profit at 14%: +14
- Loss at 6%: -6
- Overall loss of 4%: -4

### Step 3: Apply the allegation method
Using the allegation method, we can set up the following:

1. Write the profit and loss percentages:
- Profit: +14
- Loss: -6
- Overall: -4

2. Calculate the differences:
- Difference between profit (14) and overall loss (4):
\( 14 - (-4) = 14 + 4 = 18 \)
- Difference between loss (6) and overall loss (4):
\( -6 - (-4) = -6 + 4 = -2 \)

### Step 4: Set up the ratio
The ratio of quantities sold at 14% profit to the quantity sold at 6% loss is given by the differences calculated:
- Ratio = Difference from profit : Difference from loss = 18 : 2

This simplifies to:
- Ratio = 9 : 1

### Step 5: Calculate the total units
The total parts in the ratio is:
- \( 9 + 1 = 10 \) parts

### Step 6: Find the value of one part
Since the total quantity of rice is 50 kg, we can find the value of one part:
- Value of 1 part = Total quantity / Total parts = \( 50 \text{ kg} / 10 = 5 \text{ kg} \)

### Step 7: Calculate the quantities sold
Now we can find the quantities sold at each profit/loss percentage:
- Quantity sold at 14% profit = 9 parts = \( 9 \times 5 \text{ kg} = 45 \text{ kg} \)
- Quantity sold at 6% loss = 1 part = \( 1 \times 5 \text{ kg} = 5 \text{ kg} \)

### Final Answer
- Quantity sold at 14% profit: 45 kg
- Quantity sold at 6% loss: 5 kg

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