A man had 100 kgs of sugar, part of which he sold at 7% profit and rest at 17% profit. He gained 10% on the whole. How much did he sell at 7% profit?

Options

A. 65 kg
B. 35 kg
C. 30 kg
D. 70 kg

Answer

To solve the problem step by step, we can use the method of allegation to find out how much sugar was sold at 7% profit.

### Step 1: Understand the given information
- Total sugar = 100 kg
- Profit on part sold at 7% = 7%
- Profit on part sold at 17% = 17%
- Overall profit = 10%

### Step 2: Set up the allegation
We will set up an allegation to find the ratio of the quantities sold at different profit percentages.

- Profit percentages:
- Lower profit (7%) = 7%
- Overall profit = 10%
- Higher profit (17%) = 17%

### Step 3: Calculate the differences
Using the allegation method:
- Difference between higher profit and overall profit:
\( 17\% - 10\% = 7\% \)
- Difference between overall profit and lower profit:
\( 10\% - 7\% = 3\% \)

### Step 4: Set up the ratio
Now we can set up the ratio of the quantities sold at different profits:
- The ratio of quantities sold at 7% profit to those sold at 17% profit is:
- 3 (for 17%) : 7 (for 7%)

This means for every 3 parts sold at 17% profit, 7 parts are sold at 7% profit.

### Step 5: Calculate the total parts
Total parts = 3 + 7 = 10 parts.

### Step 6: Calculate the quantity sold at 7% profit
Now, we can find out how much sugar was sold at 7% profit:
- Quantity sold at 7% profit = (7 parts / 10 parts) × 100 kg
- Quantity sold at 7% profit = \( \frac{7}{10} \times 100 = 70 \) kg

### Conclusion
Thus, the man sold **70 kg** of sugar at 7% profit.